EDA_Hypothesis_Testing.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Auto Insurance Fraud EDA and Hypothesis Testing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Mary Donovan Martello"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The goal of this project was to use exploratory data analysis and statistical techniques to prove or disprove a hypothesis based on automobile claims fraud variables."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from __future__ import print_function, division\n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "# import libraries\n",
    "\n",
    "import numpy as np\n",
    "import thinkstats2\n",
    "import thinkplot\n",
    "import pandas\n",
    "from collections import Counter\n",
    "import analytic\n",
    "import random\n",
    "import scipy.stats\n",
    "import analytic\n",
    "import hinc\n",
    "from thinkstats2 import Mean, MeanVar, Var, Std, Cov\n",
    "import statsmodels.formula.api as smf\n",
    "from scipy import stats\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sn\n",
    "# importing regex module (search strings) RegEx can be used to check if a string contains the specified search pattern\n",
    "import re\n",
    "import patsy #stats\n",
    "from tabulate import tabulate\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The dataset includes 1,000 prior claim transaction records. Each record has a mix of 38 quantitative and categorical data features about the claim filed, including information on the policy, insured, and automobile, aspects of the damage incident, and elements of the claim filed. The dataset also has a feature that indicates whether fraud was reported on each observation (i.e., either Y or N)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# import data set\n",
    "dfClaims = pandas.read_csv('FradulentInsuranceClaims.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data Cleaning"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# rename difficult column names\n",
    "dfClaims.rename(columns={'capital-gains': 'capital_gains', 'capital-loss': 'capital_loss'}, inplace=True)\n",
    "#dfClaims.columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# split policy_csl into separate columns\n",
    "\n",
    "# new data frame with split value columns \n",
    "newDF = dfClaims[\"policy_csl\"].str.split(\"/\", n = 1, expand = True)\n",
    "\n",
    "# making separate csl_bodily column from new data frame \n",
    "dfClaims[\"csl_bodily\"] = newDF[0] \n",
    "  \n",
    "# making separate csl_property column from new data frame \n",
    "dfClaims[\"csl_prop\"] = newDF[1] \n",
    "  \n",
    "# Dropping old policy_csl columns \n",
    "dfClaims.drop(columns =[\"policy_csl\"], inplace = True) \n",
    "  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# change data type\n",
    "dfClaims[\"csl_bodily\"] = dfClaims[\"csl_bodily\"].astype(int)\n",
    "dfClaims[\"csl_prop\"] = dfClaims[\"csl_prop\"].astype(int)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# drop umbrella outlier observation\n",
    "#dfClaims[dfClaims.umbrella_limit >= 0]\n",
    "dfClaims.drop(dfClaims[dfClaims['umbrella_limit'] < 0].index, inplace = True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# drop empty column\n",
    "dfClaims.drop(columns =[\"_c39\"], inplace = True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# changing date format for date columns \n",
    "dfClaims[\"incident_date\"]= pandas.to_datetime(dfClaims[\"incident_date\"])\n",
    "dfClaims[\"policy_bind_date\"]= pandas.to_datetime(dfClaims[\"policy_bind_date\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Create a New Feature"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# create new column for diff in months between policy_bind_date and incident_date\n",
    "dfClaims['months_bf_incident'] = ((dfClaims.incident_date - dfClaims.policy_bind_date)/np.timedelta64(1, 'M'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Dropping old incident_date and policy_bind_date columns \n",
    "dfClaims.drop(columns =[\"incident_date\"], inplace = True)\n",
    "dfClaims.drop(columns =[\"policy_bind_date\"], inplace = True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Create Subsets for EDA"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Each record in the dataset includes a label of whether the claim was classified as fraudulent (fraud = Y) or as non-fraudulent (fraud = N). Create separate subsets of the dataset so that one subset only has records that did not have fraud transactions and another subset that only has records with fraud transactions. Use these separate subsets for EDA."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# how many fraud reported yes\n",
    "fraudY = dfClaims[dfClaims['fraud_reported'] == 'Y']\n",
    "fraudY.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(752, 39)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# how many fraud reported yes\n",
    "fraudN = dfClaims[dfClaims['fraud_reported'] == 'N']\n",
    "fraudN.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# subset for fraud reported is yes\n",
    "rowsYesFraud = dfClaims['fraud_reported'] == 'Y'\n",
    "#columnsYesFraud = ['age', 'total_claim_amount', 'witnesses']\n",
    "fraudY2 = dfClaims.loc[rowsYesFraud, ]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "# subset for fraud reported is no\n",
    "rowsNoFraud = dfClaims['fraud_reported'] == 'N'\n",
    "#columnsNoFraud = ['age', 'total_claim_amount', 'witnesses']\n",
    "fraudN2 = dfClaims.loc[rowsNoFraud, ]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Factorize Categorical Variables for EDA Use."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "# factorize categorical from strings to numberics in dfClaims df\n",
    "dfClaims['fraud_reported_f'] = pandas.factorize(dfClaims.fraud_reported)[0]\n",
    "dfClaims['policy_state_f'] = pandas.factorize(dfClaims.policy_state)[0]\n",
    "dfClaims['insured_sex_f'] = pandas.factorize(dfClaims.insured_sex)[0]\n",
    "dfClaims['insured_education_level_f'] = pandas.factorize(dfClaims.insured_education_level)[0]\n",
    "dfClaims['insured_occupation_f'] = pandas.factorize(dfClaims.insured_occupation)[0]\n",
    "dfClaims['insured_hobbies_f'] = pandas.factorize(dfClaims.insured_hobbies)[0]\n",
    "dfClaims['insured_relationship_f'] = pandas.factorize(dfClaims.insured_relationship)[0]\n",
    "dfClaims['incident_type_f'] = pandas.factorize(dfClaims.incident_type)[0]\n",
    "dfClaims['collision_type_f'] = pandas.factorize(dfClaims.collision_type)[0]\n",
    "dfClaims['incident_severity_f'] = pandas.factorize(dfClaims.incident_severity)[0]\n",
    "dfClaims['authorities_contacted_f'] = pandas.factorize(dfClaims.authorities_contacted)[0]\n",
    "dfClaims['incident_state_f'] = pandas.factorize(dfClaims.incident_state)[0]\n",
    "dfClaims['incident_city_f'] = pandas.factorize(dfClaims.incident_city)[0]\n",
    "dfClaims['property_damage_f'] = pandas.factorize(dfClaims.property_damage)[0]\n",
    "dfClaims['police_report_available_f'] = pandas.factorize(dfClaims.police_report_available)[0]\n",
    "dfClaims['auto_make_f'] = pandas.factorize(dfClaims.auto_make)[0]\n",
    "dfClaims['auto_model_f'] = pandas.factorize(dfClaims.auto_model)[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# factorize categorical from strings to numberics in fraudY2 df\n",
    "\n",
    "pandas.set_option('mode.chained_assignment', None)\n",
    "\n",
    "fraudY2['fraud_reported_f'] = pandas.factorize(fraudY2.fraud_reported)[0]\n",
    "fraudY2['policy_state_f'] = pandas.factorize(fraudY2.policy_state)[0]\n",
    "fraudY2['insured_sex_f'] = pandas.factorize(fraudY2.insured_sex)[0]\n",
    "fraudY2['insured_education_level_f'] = pandas.factorize(fraudY2.insured_education_level)[0]\n",
    "fraudY2['insured_occupation_f'] = pandas.factorize(fraudY2.insured_occupation)[0]\n",
    "fraudY2['insured_hobbies_f'] = pandas.factorize(fraudY2.insured_hobbies)[0]\n",
    "fraudY2['insured_relationship_f'] = pandas.factorize(fraudY2.insured_relationship)[0]\n",
    "fraudY2['incident_type_f'] = pandas.factorize(fraudY2.incident_type)[0]\n",
    "fraudY2['collision_type_f'] = pandas.factorize(fraudY2.collision_type)[0]\n",
    "fraudY2['incident_severity_f'] = pandas.factorize(fraudY2.incident_severity)[0]\n",
    "fraudY2['authorities_contacted_f'] = pandas.factorize(fraudY2.authorities_contacted)[0]\n",
    "fraudY2['incident_state_f'] = pandas.factorize(fraudY2.incident_state)[0]\n",
    "fraudY2['incident_city_f'] = pandas.factorize(fraudY2.incident_city)[0]\n",
    "fraudY2['property_damage_f'] = pandas.factorize(fraudY2.property_damage)[0]\n",
    "fraudY2['police_report_available_f'] = pandas.factorize(fraudY2.police_report_available)[0]\n",
    "fraudY2['auto_make_f'] = pandas.factorize(fraudY2.auto_make)[0]\n",
    "fraudY2['auto_model_f'] = pandas.factorize(fraudY2.auto_model)[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "# factorize categorical from strings to numberics in fraudN2 df\n",
    "\n",
    "pandas.set_option('mode.chained_assignment', None)\n",
    "\n",
    "fraudN2['fraud_reported_f'] = pandas.factorize(fraudN2.fraud_reported)[0]\n",
    "fraudN2['policy_state_f'] = pandas.factorize(fraudN2.policy_state)[0]\n",
    "fraudN2['insured_sex_f'] = pandas.factorize(fraudN2.insured_sex)[0]\n",
    "fraudN2['insured_education_level_f'] = pandas.factorize(fraudN2.insured_education_level)[0]\n",
    "fraudN2['insured_occupation_f'] = pandas.factorize(fraudN2.insured_occupation)[0]\n",
    "fraudN2['insured_hobbies_f'] = pandas.factorize(fraudN2.insured_hobbies)[0]\n",
    "fraudN2['insured_relationship_f'] = pandas.factorize(fraudN2.insured_relationship)[0]\n",
    "fraudN2['incident_type_f'] = pandas.factorize(fraudN2.incident_type)[0]\n",
    "fraudN2['collision_type_f'] = pandas.factorize(fraudN2.collision_type)[0]\n",
    "fraudN2['incident_severity_f'] = pandas.factorize(fraudN2.incident_severity)[0]\n",
    "fraudN2['authorities_contacted_f'] = pandas.factorize(fraudN2.authorities_contacted)[0]\n",
    "fraudN2['incident_state_f'] = pandas.factorize(fraudN2.incident_state)[0]\n",
    "fraudN2['incident_city_f'] = pandas.factorize(fraudN2.incident_city)[0]\n",
    "fraudN2['property_damage_f'] = pandas.factorize(fraudN2.property_damage)[0]\n",
    "fraudN2['police_report_available_f'] = pandas.factorize(fraudN2.police_report_available)[0]\n",
    "fraudN2['auto_make_f'] = pandas.factorize(fraudN2.auto_make)[0]\n",
    "fraudN2['auto_model_f'] = pandas.factorize(fraudN2.auto_model)[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Histograms"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# full dataset\n",
    "totalClaimAmt = np.around(dfClaims.total_claim_amount, decimals=-4)\n",
    "histTotClaimAmt = thinkstats2.Hist(totalClaimAmt, label='Total Claim Amount')\n",
    "thinkplot.Hist(histTotClaimAmt)\n",
    "thinkplot.Config(xlabel='Total Claim Amount', ylabel='Count')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# fraud subset\n",
    "totalClaimAmtY = np.around(fraudY2.total_claim_amount, decimals=-4)\n",
    "hist = thinkstats2.Hist(totalClaimAmtY, label='Total Claim Amount - Fraud Reported')\n",
    "thinkplot.Hist(hist)\n",
    "thinkplot.Config(xlabel='Total Claim Amount', ylabel='Count')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#non-fraud subset\n",
    "totalClaimAmtN = np.around(fraudN2.total_claim_amount, decimals=-4)\n",
    "hist = thinkstats2.Hist(totalClaimAmtN, label='Total Claim Amount - No Fraud Reported')\n",
    "thinkplot.Hist(hist)\n",
    "thinkplot.Config(xlabel='Total Claim Amount', ylabel='Count')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# full dataset\n",
    "# after filtering out the negative outlier\n",
    "histUmbrella = thinkstats2.Hist(dfClaims.umbrella_limit, label='Umbrella Limit')\n",
    "thinkplot.Hist(histUmbrella)\n",
    "thinkplot.Config(xlabel='Umbrella Limit', ylabel='Count')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# fraud subset\n",
    "# after filtering out the negative outlier\n",
    "histUmbrella = thinkstats2.Hist(fraudY2.umbrella_limit, label='Umbrella Limit - Fraud Reported')\n",
    "thinkplot.Hist(histUmbrella)\n",
    "thinkplot.Config(xlabel='Umbrella Limit', ylabel='Count')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# non-fraud subset\n",
    "# after filtering out the negative outlier\n",
    "histUmbrella = thinkstats2.Hist(fraudN2.umbrella_limit, label='Umbrella Limit - No Fraud Reported')\n",
    "thinkplot.Hist(histUmbrella)\n",
    "thinkplot.Config(xlabel='Umbrella Limit', ylabel='Count')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# full dataset\n",
    "monthsBfInc = np.around(dfClaims.months_bf_incident, decimals=-1)\n",
    "hist = thinkstats2.Hist(monthsBfInc, label='Months before incident')\n",
    "thinkplot.Hist(hist)\n",
    "thinkplot.Config(xlabel='Months Before Incident', ylabel='Count')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# fraud subset\n",
    "monthsBfIncY = np.around(fraudY2.months_bf_incident, decimals=-1)\n",
    "hist = thinkstats2.Hist(monthsBfIncY, label='Months before incident- Fraud Reported')\n",
    "thinkplot.Hist(hist)\n",
    "thinkplot.Config(xlabel='Months Before Incident', ylabel='Count')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# non-fraud subset\n",
    "monthsBfIncN = np.around(fraudN2.months_bf_incident, decimals=-1)\n",
    "hist = thinkstats2.Hist(monthsBfIncN, label='Months before incident- No Fraud Reported')\n",
    "thinkplot.Hist(hist)\n",
    "thinkplot.Config(xlabel='Months Before Incident', ylabel='Count')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# full dataset\n",
    "histWitnesses = thinkstats2.Hist(dfClaims.witnesses, label='Witnesses')\n",
    "thinkplot.Hist(histWitnesses)\n",
    "thinkplot.Config(xlabel='Witnesses', ylabel='Count')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# fraud subset\n",
    "histWitnesses = thinkstats2.Hist(fraudY2.witnesses, label='Witnesses- Fraud Reported')\n",
    "thinkplot.Hist(histWitnesses)\n",
    "thinkplot.Config(xlabel='Witnesses', ylabel='Count')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# non-fraud subset\n",
    "histWitnesses = thinkstats2.Hist(fraudN2.witnesses, label='Witnesses- No Fraud Reported')\n",
    "thinkplot.Hist(histWitnesses)\n",
    "thinkplot.Config(xlabel='Witnesses', ylabel='Count')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# full dataset\n",
    "histPolDeduct = thinkstats2.Hist(dfClaims.policy_deductable, label='Policy Deductible')\n",
    "thinkplot.Hist(histPolDeduct)\n",
    "thinkplot.Config(xlabel='Policy Deductible', ylabel='Count')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# fraud subset\n",
    "histPolDeduct = thinkstats2.Hist(fraudY2.policy_deductable, label='Policy Deductible - Fraud Reported')\n",
    "thinkplot.Hist(histPolDeduct)\n",
    "thinkplot.Config(xlabel='Policy Deductible', ylabel='Count')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# non-fraud subset\n",
    "histPolDeduct = thinkstats2.Hist(fraudN2.policy_deductable, label='Policy Deductible - No Fraud Reported')\n",
    "thinkplot.Hist(histPolDeduct)\n",
    "thinkplot.Config(xlabel='Policy Deductible', ylabel='Count')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# full dataset\n",
    "histIncSev = thinkstats2.Hist(dfClaims.incident_severity, label='Incident Severity')\n",
    "thinkplot.Hist(histIncSev)\n",
    "thinkplot.Config(xlabel='Incident Severity', ylabel='Count')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# fraud subset\n",
    "histIncSev = thinkstats2.Hist(fraudY2.incident_severity, label='Incident Severity - Fraud Reported')\n",
    "thinkplot.Hist(histIncSev)\n",
    "thinkplot.Config(xlabel='Incident Severity', ylabel='Count')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# non-fraud subset\n",
    "histIncSev = thinkstats2.Hist(fraudN2.incident_severity, label='Incident Severity - No Fraud Reported')\n",
    "thinkplot.Hist(histIncSev)\n",
    "thinkplot.Config(xlabel='Incident Severity', ylabel='Count')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Statistical Analysis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>months_bf_incident</th>\n",
       "      <th>total_claim_amount</th>\n",
       "      <th>vehicle_claim</th>\n",
       "      <th>witnesses</th>\n",
       "      <th>number_of_vehicles_involved</th>\n",
       "      <th>policy_deductable</th>\n",
       "      <th>umbrella_limit</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>999.000000</td>\n",
       "      <td>999.000000</td>\n",
       "      <td>999.000000</td>\n",
       "      <td>999.000000</td>\n",
       "      <td>999.000000</td>\n",
       "      <td>999.000000</td>\n",
       "      <td>9.990000e+02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>155.622634</td>\n",
       "      <td>52720.500501</td>\n",
       "      <td>37898.368368</td>\n",
       "      <td>1.487487</td>\n",
       "      <td>1.839840</td>\n",
       "      <td>1136.636637</td>\n",
       "      <td>1.103103e+06</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>88.269144</td>\n",
       "      <td>26382.199299</td>\n",
       "      <td>18870.924206</td>\n",
       "      <td>1.111785</td>\n",
       "      <td>1.019044</td>\n",
       "      <td>611.839681</td>\n",
       "      <td>2.297594e+06</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>-0.657098</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>70.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>500.000000</td>\n",
       "      <td>0.000000e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>81.545822</td>\n",
       "      <td>41775.000000</td>\n",
       "      <td>30275.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>500.000000</td>\n",
       "      <td>0.000000e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>153.662293</td>\n",
       "      <td>57970.000000</td>\n",
       "      <td>42080.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1000.000000</td>\n",
       "      <td>0.000000e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>232.185466</td>\n",
       "      <td>70550.000000</td>\n",
       "      <td>50775.000000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>2000.000000</td>\n",
       "      <td>0.000000e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>301.344997</td>\n",
       "      <td>114920.000000</td>\n",
       "      <td>79560.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>2000.000000</td>\n",
       "      <td>1.000000e+07</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       months_bf_incident  total_claim_amount  vehicle_claim   witnesses  \\\n",
       "count          999.000000          999.000000     999.000000  999.000000   \n",
       "mean           155.622634        52720.500501   37898.368368    1.487487   \n",
       "std             88.269144        26382.199299   18870.924206    1.111785   \n",
       "min             -0.657098          100.000000      70.000000    0.000000   \n",
       "25%             81.545822        41775.000000   30275.000000    1.000000   \n",
       "50%            153.662293        57970.000000   42080.000000    1.000000   \n",
       "75%            232.185466        70550.000000   50775.000000    2.000000   \n",
       "max            301.344997       114920.000000   79560.000000    3.000000   \n",
       "\n",
       "       number_of_vehicles_involved  policy_deductable  umbrella_limit  \n",
       "count                   999.000000         999.000000    9.990000e+02  \n",
       "mean                      1.839840        1136.636637    1.103103e+06  \n",
       "std                       1.019044         611.839681    2.297594e+06  \n",
       "min                       1.000000         500.000000    0.000000e+00  \n",
       "25%                       1.000000         500.000000    0.000000e+00  \n",
       "50%                       1.000000        1000.000000    0.000000e+00  \n",
       "75%                       3.000000        2000.000000    0.000000e+00  \n",
       "max                       4.000000        2000.000000    1.000000e+07  "
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create new dataset with quantitative variables\n",
    "dfClaims_quant = dfClaims.filter(['months_bf_incident', 'total_claim_amount', 'witnesses', 'policy_deductable', 'umbrella_limit'], axis=1)\n",
    "dfClaims_quant.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>months_bf_incident</th>\n",
       "      <th>total_claim_amount</th>\n",
       "      <th>vehicle_claim</th>\n",
       "      <th>witnesses</th>\n",
       "      <th>number_of_vehicles_involved</th>\n",
       "      <th>policy_deductable</th>\n",
       "      <th>umbrella_limit</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>247.000000</td>\n",
       "      <td>247.000000</td>\n",
       "      <td>247.000000</td>\n",
       "      <td>247.000000</td>\n",
       "      <td>247.000000</td>\n",
       "      <td>247.000000</td>\n",
       "      <td>2.470000e+02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>155.847076</td>\n",
       "      <td>60302.105263</td>\n",
       "      <td>43533.643725</td>\n",
       "      <td>1.582996</td>\n",
       "      <td>1.931174</td>\n",
       "      <td>1151.821862</td>\n",
       "      <td>1.336032e+06</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>87.874222</td>\n",
       "      <td>20746.279567</td>\n",
       "      <td>14849.388907</td>\n",
       "      <td>1.066962</td>\n",
       "      <td>1.047315</td>\n",
       "      <td>628.123674</td>\n",
       "      <td>2.494799e+06</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>2.694100</td>\n",
       "      <td>2860.000000</td>\n",
       "      <td>2080.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>500.000000</td>\n",
       "      <td>0.000000e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>82.958582</td>\n",
       "      <td>51910.000000</td>\n",
       "      <td>37170.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>500.000000</td>\n",
       "      <td>0.000000e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>152.380952</td>\n",
       "      <td>61290.000000</td>\n",
       "      <td>44800.000000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1000.000000</td>\n",
       "      <td>0.000000e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>233.368242</td>\n",
       "      <td>72665.000000</td>\n",
       "      <td>52080.000000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>2000.000000</td>\n",
       "      <td>0.000000e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>299.767962</td>\n",
       "      <td>112320.000000</td>\n",
       "      <td>77760.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>2000.000000</td>\n",
       "      <td>1.000000e+07</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       months_bf_incident  total_claim_amount  vehicle_claim   witnesses  \\\n",
       "count          247.000000          247.000000     247.000000  247.000000   \n",
       "mean           155.847076        60302.105263   43533.643725    1.582996   \n",
       "std             87.874222        20746.279567   14849.388907    1.066962   \n",
       "min              2.694100         2860.000000    2080.000000    0.000000   \n",
       "25%             82.958582        51910.000000   37170.000000    1.000000   \n",
       "50%            152.380952        61290.000000   44800.000000    2.000000   \n",
       "75%            233.368242        72665.000000   52080.000000    2.000000   \n",
       "max            299.767962       112320.000000   77760.000000    3.000000   \n",
       "\n",
       "       number_of_vehicles_involved  policy_deductable  umbrella_limit  \n",
       "count                   247.000000         247.000000    2.470000e+02  \n",
       "mean                      1.931174        1151.821862    1.336032e+06  \n",
       "std                       1.047315         628.123674    2.494799e+06  \n",
       "min                       1.000000         500.000000    0.000000e+00  \n",
       "25%                       1.000000         500.000000    0.000000e+00  \n",
       "50%                       1.000000        1000.000000    0.000000e+00  \n",
       "75%                       3.000000        2000.000000    0.000000e+00  \n",
       "max                       4.000000        2000.000000    1.000000e+07  "
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create new dataset with quantitative variables - fraud reported\n",
    "fraudY2_quant = fraudY2.filter(['months_bf_incident', 'total_claim_amount', 'vehicle_claim', 'witnesses', 'number_of_vehicles_involved', 'policy_deductable', 'umbrella_limit'], axis=1)\n",
    "fraudY2_quant.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>months_bf_incident</th>\n",
       "      <th>total_claim_amount</th>\n",
       "      <th>vehicle_claim</th>\n",
       "      <th>witnesses</th>\n",
       "      <th>number_of_vehicles_involved</th>\n",
       "      <th>policy_deductable</th>\n",
       "      <th>umbrella_limit</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>752.000000</td>\n",
       "      <td>752.000000</td>\n",
       "      <td>752.000000</td>\n",
       "      <td>752.000000</td>\n",
       "      <td>752.000000</td>\n",
       "      <td>752.000000</td>\n",
       "      <td>7.520000e+02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>155.548915</td>\n",
       "      <td>50230.265957</td>\n",
       "      <td>36047.420213</td>\n",
       "      <td>1.456117</td>\n",
       "      <td>1.809840</td>\n",
       "      <td>1131.648936</td>\n",
       "      <td>1.026596e+06</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>88.456660</td>\n",
       "      <td>27547.003973</td>\n",
       "      <td>19675.642596</td>\n",
       "      <td>1.125040</td>\n",
       "      <td>1.008491</td>\n",
       "      <td>606.738410</td>\n",
       "      <td>2.225463e+06</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>-0.657098</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>70.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>500.000000</td>\n",
       "      <td>0.000000e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>80.428756</td>\n",
       "      <td>34650.000000</td>\n",
       "      <td>25200.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>500.000000</td>\n",
       "      <td>0.000000e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>154.762931</td>\n",
       "      <td>56475.000000</td>\n",
       "      <td>41190.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1000.000000</td>\n",
       "      <td>0.000000e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>232.111542</td>\n",
       "      <td>69480.000000</td>\n",
       "      <td>49935.000000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>2000.000000</td>\n",
       "      <td>0.000000e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>301.344997</td>\n",
       "      <td>114920.000000</td>\n",
       "      <td>79560.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>2000.000000</td>\n",
       "      <td>1.000000e+07</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       months_bf_incident  total_claim_amount  vehicle_claim   witnesses  \\\n",
       "count          752.000000          752.000000     752.000000  752.000000   \n",
       "mean           155.548915        50230.265957   36047.420213    1.456117   \n",
       "std             88.456660        27547.003973   19675.642596    1.125040   \n",
       "min             -0.657098          100.000000      70.000000    0.000000   \n",
       "25%             80.428756        34650.000000   25200.000000    0.000000   \n",
       "50%            154.762931        56475.000000   41190.000000    1.000000   \n",
       "75%            232.111542        69480.000000   49935.000000    2.000000   \n",
       "max            301.344997       114920.000000   79560.000000    3.000000   \n",
       "\n",
       "       number_of_vehicles_involved  policy_deductable  umbrella_limit  \n",
       "count                   752.000000         752.000000    7.520000e+02  \n",
       "mean                      1.809840        1131.648936    1.026596e+06  \n",
       "std                       1.008491         606.738410    2.225463e+06  \n",
       "min                       1.000000         500.000000    0.000000e+00  \n",
       "25%                       1.000000         500.000000    0.000000e+00  \n",
       "50%                       1.000000        1000.000000    0.000000e+00  \n",
       "75%                       3.000000        2000.000000    0.000000e+00  \n",
       "max                       4.000000        2000.000000    1.000000e+07  "
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create new dataset with quantitative variables - no fraud reported\n",
    "fraudN2_quant = fraudN2.filter(['months_bf_incident', 'total_claim_amount', 'vehicle_claim', 'witnesses', 'number_of_vehicles_involved', 'policy_deductable', 'umbrella_limit'], axis=1)\n",
    "fraudN2_quant.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Kurtosis and Skew Statistics**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "# compute kurtosis and skew statistics\n",
    "monthsStats = scipy.stats.describe(dfClaims.months_bf_incident, ddof=1, bias=False)\n",
    "totalClaimStats = scipy.stats.describe(dfClaims.total_claim_amount, ddof=1, bias=False)\n",
    "vehicleClaimStats = scipy.stats.describe(dfClaims.vehicle_claim, ddof=1, bias=False)\n",
    "numVehiclesStats = scipy.stats.describe(dfClaims.number_of_vehicles_involved, ddof=1, bias=False)\n",
    "umbrellaStats = scipy.stats.describe(dfClaims.umbrella_limit, ddof=1, bias=False)\n",
    "deductibleStats = scipy.stats.describe(dfClaims.policy_deductable, ddof=1, bias=False)\n",
    "witnessesStats = scipy.stats.describe(dfClaims.witnesses, ddof=1, bias=False)\n",
    "monthsStatsY = scipy.stats.describe(fraudY2.months_bf_incident, ddof=1, bias=False)\n",
    "totalClaimStatsY = scipy.stats.describe(fraudY2.total_claim_amount, ddof=1, bias=False)\n",
    "vehicleClaimStatsY = scipy.stats.describe(fraudY2.vehicle_claim, ddof=1, bias=False)\n",
    "numVehiclesStatsY = scipy.stats.describe(fraudY2.number_of_vehicles_involved, ddof=1, bias=False)\n",
    "umbrellaStatsY = scipy.stats.describe(fraudY2.umbrella_limit, ddof=1, bias=False)\n",
    "deductibleStatsY = scipy.stats.describe(fraudY2.policy_deductable, ddof=1, bias=False)\n",
    "witnessesStatsY = scipy.stats.describe(fraudY2.witnesses, ddof=1, bias=False)\n",
    "monthsStatsN = scipy.stats.describe(fraudN2.months_bf_incident, ddof=1, bias=False)\n",
    "totalClaimStatsN = scipy.stats.describe(fraudN2.total_claim_amount, ddof=1, bias=False)\n",
    "vehicleClaimStatsN = scipy.stats.describe(fraudN2.vehicle_claim, ddof=1, bias=False)\n",
    "numVehiclesStatsN = scipy.stats.describe(fraudN2.number_of_vehicles_involved, ddof=1, bias=False)\n",
    "umbrellaStatsN = scipy.stats.describe(fraudN2.umbrella_limit, ddof=1, bias=False)\n",
    "deductibleStatsN = scipy.stats.describe(fraudN2.policy_deductable, ddof=1, bias=False)\n",
    "witnessesStatsN = scipy.stats.describe(fraudN2.witnesses, ddof=1, bias=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "| Variable               |       Mode |         Variance |      Range |   Skewness |   Kurtosis |\n",
      "|------------------------+------------+------------------+------------+------------+------------|\n",
      "| Months before incident |    62.3914 |   7791.44        |    302.002 | -0.0508087 |  -1.20225  |\n",
      "| Total Claim Amount     | 59400      |      6.9602e+08  | 114820     | -0.595646  |  -0.453894 |\n",
      "| Vehicle Claim Amounts  |  5040      |      3.56112e+08 |  79490     | -0.622627  |  -0.446648 |\n",
      "| Vehicles Involved      |     1      |      1.03845     |      3     |  0.501009  |  -1.50205  |\n",
      "| Umbrella Limit         |     0      |      5.27894e+12 |      1e+07 |  1.8061    |   1.78799  |\n",
      "| Deductable Amount      |  1000      | 374348           |   1500     |  0.476426  |  -1.37821  |\n",
      "| Witnesses              |     1      |      1.23607     |      3     |  0.0183986 |  -1.34473  |\n"
     ]
    }
   ],
   "source": [
    "from tabulate import tabulate\n",
    "statsQuant = [[\"Months before incident\", dfClaims.months_bf_incident.mode(), dfClaims.months_bf_incident.var(), dfClaims.months_bf_incident.max() - dfClaims.months_bf_incident.min(), monthsStats.skewness, monthsStats.kurtosis], \n",
    "              ['Total Claim Amount', dfClaims.total_claim_amount.mode(), dfClaims.total_claim_amount.var(), dfClaims.total_claim_amount.max() - dfClaims.total_claim_amount.min(), totalClaimStats.skewness, totalClaimStats.kurtosis], \n",
    "              ['Vehicle Claim Amounts', dfClaims.vehicle_claim.mode(), dfClaims.vehicle_claim.var(), dfClaims.vehicle_claim.max() - dfClaims.vehicle_claim.min(), vehicleClaimStats.skewness, vehicleClaimStats.kurtosis], \n",
    "              ['Vehicles Involved', dfClaims.number_of_vehicles_involved.mode(), dfClaims.number_of_vehicles_involved.var(), dfClaims.number_of_vehicles_involved.max() - dfClaims.number_of_vehicles_involved.min(), numVehiclesStats.skewness, numVehiclesStats.kurtosis], \n",
    "              ['Umbrella Limit', dfClaims.umbrella_limit.mode(), dfClaims.umbrella_limit.var(), dfClaims.umbrella_limit.max() - dfClaims.umbrella_limit.min(), umbrellaStats.skewness, umbrellaStats.kurtosis], \n",
    "              ['Deductable Amount', dfClaims.policy_deductable.mode(), dfClaims.policy_deductable.var(), dfClaims.policy_deductable.max() - dfClaims.policy_deductable.min(), deductibleStats.skewness, deductibleStats.kurtosis], \n",
    "              ['Witnesses', dfClaims.witnesses.mode(), dfClaims.witnesses.var(), dfClaims.witnesses.max() - dfClaims.witnesses.min(), witnessesStats.skewness, witnessesStats.kurtosis]]\n",
    "tableQuant = tabulate(statsQuant, headers=['Variable', 'Mode', 'Variance', 'Range', 'Skewness', 'Kurtosis'], tablefmt='orgtbl')\n",
    "print(tableQuant)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "| Variable               | Mode           |         Variance |      Range |   Skewness |   Kurtosis |\n",
      "|------------------------+----------------+------------------+------------+------------+------------|\n",
      "| Months before incident | 0    62.391425 |   7721.88        |    297.074 |  -0.103498 |   -1.18728 |\n",
      "|                        | dtype: float64 |                  |            |            |            |\n",
      "| Total Claim Amount     | 0    55000     |      4.30408e+08 | 109460     |  -0.820915 |    1.39238 |\n",
      "|                        | 1    59400     |                  |            |            |            |\n",
      "|                        | 2    75400     |                  |            |            |            |\n",
      "|                        | dtype: int64   |                  |            |            |            |\n",
      "| Vehicle Claim Amounts  | 0    38850     |      2.20504e+08 |  75680     |  -0.843381 |    1.49067 |\n",
      "|                        | 1    45360     |                  |            |            |            |\n",
      "|                        | 2    46800     |                  |            |            |            |\n",
      "|                        | 3    52080     |                  |            |            |            |\n",
      "|                        | dtype: int64   |                  |            |            |            |\n",
      "| Vehicles Involved      | 0    1         |      1.09687     |      3     |   0.373853 |   -1.56837 |\n",
      "|                        | dtype: int64   |                  |            |            |            |\n",
      "| Umbrella Limit         | 0    0         |      6.22402e+12 |      1e+07 |   1.56778  |    1.03125 |\n",
      "|                        | dtype: int64   |                  |            |            |            |\n",
      "| Deductable Amount      | 0    500       | 394539           |   1500     |   0.414332 |   -1.49377 |\n",
      "|                        | dtype: int64   |                  |            |            |            |\n",
      "| Witnesses              | 0    2         |      1.13841     |      3     |  -0.11723  |   -1.21972 |\n",
      "|                        | dtype: int64   |                  |            |            |            |\n"
     ]
    }
   ],
   "source": [
    "statsQuantY = [[\"Months before incident\", fraudY2.months_bf_incident.mode(), fraudY2.months_bf_incident.var(), fraudY2.months_bf_incident.max() - fraudY2.months_bf_incident.min(), monthsStatsY.skewness, monthsStatsY.kurtosis], \n",
    "              ['Total Claim Amount', fraudY2.total_claim_amount.mode(), fraudY2.total_claim_amount.var(), fraudY2.total_claim_amount.max() - fraudY2.total_claim_amount.min(), totalClaimStatsY.skewness, totalClaimStatsY.kurtosis], \n",
    "              ['Vehicle Claim Amounts', fraudY2.vehicle_claim.mode(), fraudY2.vehicle_claim.var(), fraudY2.vehicle_claim.max() - fraudY2.vehicle_claim.min(), vehicleClaimStatsY.skewness, vehicleClaimStatsY.kurtosis], \n",
    "              ['Vehicles Involved', fraudY2.number_of_vehicles_involved.mode(), fraudY2.number_of_vehicles_involved.var(), fraudY2.number_of_vehicles_involved.max() - fraudY2.number_of_vehicles_involved.min(), numVehiclesStatsY.skewness, numVehiclesStatsY.kurtosis], \n",
    "              ['Umbrella Limit', fraudY2.umbrella_limit.mode(), fraudY2.umbrella_limit.var(), fraudY2.umbrella_limit.max() - fraudY2.umbrella_limit.min(), umbrellaStatsY.skewness, umbrellaStatsY.kurtosis], \n",
    "              ['Deductable Amount', fraudY2.policy_deductable.mode(), fraudY2.policy_deductable.var(), fraudY2.policy_deductable.max() - fraudY2.policy_deductable.min(), deductibleStatsY.skewness, deductibleStatsY.kurtosis], \n",
    "              ['Witnesses', fraudY2.witnesses.mode(), fraudY2.witnesses.var(), fraudY2.witnesses.max() - fraudY2.witnesses.min(), witnessesStatsY.skewness, witnessesStatsY.kurtosis]]\n",
    "tableQuantY = tabulate(statsQuantY, headers=['Variable', 'Mode', 'Variance', 'Range', 'Skewness', 'Kurtosis'], tablefmt='orgtbl')\n",
    "print(tableQuantY)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "| Variable               | Mode             |         Variance |      Range |   Skewness |   Kurtosis |\n",
      "|------------------------+------------------+------------------+------------+------------+------------|\n",
      "| Months before incident | 0      18.792994 |   7824.58        |    302.002 | -0.0340399 |  -1.20685  |\n",
      "|                        | 1      24.772583 |                  |            |            |            |\n",
      "|                        | 2      53.619171 |                  |            |            |            |\n",
      "|                        | 3      54.243414 |                  |            |            |            |\n",
      "|                        | 4      62.161441 |                  |            |            |            |\n",
      "|                        | 5      81.677242 |                  |            |            |            |\n",
      "|                        | 6      94.424937 |                  |            |            |            |\n",
      "|                        | 7      94.753486 |                  |            |            |            |\n",
      "|                        | 8     112.363704 |                  |            |            |            |\n",
      "|                        | 9     114.827820 |                  |            |            |            |\n",
      "|                        | 10    145.875685 |                  |            |            |            |\n",
      "|                        | 11    160.758948 |                  |            |            |            |\n",
      "|                        | 12    175.543646 |                  |            |            |            |\n",
      "|                        | 13    204.225959 |                  |            |            |            |\n",
      "|                        | 14    214.608103 |                  |            |            |            |\n",
      "|                        | 15    232.185466 |                  |            |            |            |\n",
      "|                        | 16    254.625352 |                  |            |            |            |\n",
      "|                        | 17    270.691390 |                  |            |            |            |\n",
      "|                        | 18    273.188361 |                  |            |            |            |\n",
      "|                        | 19    279.135095 |                  |            |            |            |\n",
      "|                        | dtype: float64   |                  |            |            |            |\n",
      "| Total Claim Amount     | 0    2640        |      7.58837e+08 | 114820     | -0.469569  |  -0.789692 |\n",
      "|                        | 1    3190        |                  |            |            |            |\n",
      "|                        | 2    4320        |                  |            |            |            |\n",
      "|                        | dtype: int64     |                  |            |            |            |\n",
      "| Vehicle Claim Amounts  | 0    5040        |      3.87131e+08 |  79490     | -0.49703   |  -0.798707 |\n",
      "|                        | dtype: int64     |                  |            |            |            |\n",
      "| Vehicles Involved      | 0    1           |      1.01705     |      3     |  0.543977  |  -1.47803  |\n",
      "|                        | dtype: int64     |                  |            |            |            |\n",
      "| Umbrella Limit         | 0    0           |      4.95269e+12 |      1e+07 |  1.89682   |   2.0992   |\n",
      "|                        | dtype: int64     |                  |            |            |            |\n",
      "| Deductable Amount      | 0    1000        | 368131           |   1500     |  0.498183  |  -1.33809  |\n",
      "|                        | dtype: int64     |                  |            |            |            |\n",
      "| Witnesses              | 0    0           |      1.26571     |      3     |  0.0646493 |  -1.37144  |\n",
      "|                        | dtype: int64     |                  |            |            |            |\n"
     ]
    }
   ],
   "source": [
    "statsQuantN = [[\"Months before incident\", fraudN2.months_bf_incident.mode(), fraudN2.months_bf_incident.var(), fraudN2.months_bf_incident.max() - fraudN2.months_bf_incident.min(), monthsStatsN.skewness, monthsStatsN.kurtosis], \n",
    "              ['Total Claim Amount', fraudN2.total_claim_amount.mode(), fraudN2.total_claim_amount.var(), fraudN2.total_claim_amount.max() - fraudN2.total_claim_amount.min(), totalClaimStatsN.skewness, totalClaimStatsN.kurtosis], \n",
    "              ['Vehicle Claim Amounts', fraudN2.vehicle_claim.mode(), fraudN2.vehicle_claim.var(), fraudN2.vehicle_claim.max() - fraudN2.vehicle_claim.min(), vehicleClaimStatsN.skewness, vehicleClaimStatsN.kurtosis], \n",
    "              ['Vehicles Involved', fraudN2.number_of_vehicles_involved.mode(), fraudN2.number_of_vehicles_involved.var(), fraudN2.number_of_vehicles_involved.max() - fraudN2.number_of_vehicles_involved.min(), numVehiclesStatsN.skewness, numVehiclesStatsN.kurtosis], \n",
    "              ['Umbrella Limit', fraudN2.umbrella_limit.mode(), fraudN2.umbrella_limit.var(), fraudN2.umbrella_limit.max() - fraudN2.umbrella_limit.min(), umbrellaStatsN.skewness, umbrellaStatsN.kurtosis], \n",
    "              ['Deductable Amount', fraudN2.policy_deductable.mode(), fraudN2.policy_deductable.var(), fraudN2.policy_deductable.max() - fraudN2.policy_deductable.min(), deductibleStatsN.skewness, deductibleStatsN.kurtosis], \n",
    "              ['Witnesses', fraudN2.witnesses.mode(), fraudN2.witnesses.var(), fraudN2.witnesses.max() - fraudN2.witnesses.min(), witnessesStatsN.skewness, witnessesStatsN.kurtosis]]\n",
    "tableQuantN = tabulate(statsQuantN, headers=['Variable', 'Mode', 'Variance', 'Range', 'Skewness', 'Kurtosis'], tablefmt='orgtbl')\n",
    "print(tableQuantN)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Probability Mass Function**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# pmf\n",
    "# Here are the distributions of incident severity for fraud reported and fraud not reported.\n",
    "fraudY_pmfSev = thinkstats2.Pmf(fraudY2.incident_severity_f, label='Fraud Reported')\n",
    "fraudN_pmfSev = thinkstats2.Pmf(fraudN2.incident_severity_f, label='Fraud Not Reported')\n",
    "\n",
    "# code to plot bar graphs and step function PMFs.\n",
    "width=0.45\n",
    "axis = [-1, 4, -0.20, 0.99]\n",
    "thinkplot.PrePlot(2, cols=2)\n",
    "thinkplot.Hist(fraudY_pmfSev, align='right', width=width)\n",
    "thinkplot.Hist(fraudN_pmfSev, align='left', width=width)\n",
    "thinkplot.Config(xlabel='incident_severity_f', ylabel='PMF', axis=axis)\n",
    "\n",
    "thinkplot.PrePlot(2)\n",
    "thinkplot.SubPlot(2)\n",
    "thinkplot.Pmfs([fraudY_pmfSev, fraudN_pmfSev])\n",
    "thinkplot.Config(xlabel='incident_severity_f', axis=axis)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Cumulative Distribution Function**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot cdf = fraud reported\n",
    "cdfTCY = thinkstats2.Cdf(fraudY2.total_claim_amount, label='total_claim_amount - fraud reported')\n",
    "thinkplot.Cdf(cdfTCY)\n",
    "thinkplot.Config(xlabel='total_claim_amount', ylabel='CDF', loc='upper left')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot cdf = no fraud reported\n",
    "cdfTCN = thinkstats2.Cdf(fraudN2.total_claim_amount, label='total_claim_amount no fraud reported')\n",
    "thinkplot.Cdf(cdfTCN)\n",
    "thinkplot.Config(xlabel='total_claim_amount', ylabel='CDF', loc='upper left')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Probability Plot**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((array([-2.77005632, -2.46756954, -2.29577765, -2.17308639, -2.07637768,\n",
       "         -1.99590511, -1.92660022, -1.86547617, -1.81061863, -1.76072402,\n",
       "         -1.71486302, -1.6723488 , -1.63265879, -1.59538576, -1.56020597,\n",
       "         -1.52685756, -1.49512565, -1.46483159, -1.43582519, -1.40797894,\n",
       "         -1.38118357, -1.35534475, -1.33038042, -1.30621874, -1.28279645,\n",
       "         -1.26005751, -1.23795207, -1.21643554, -1.1954679 , -1.17501306,\n",
       "         -1.15503839, -1.13551422, -1.11641358, -1.09771179, -1.07938624,\n",
       "         -1.0614162 , -1.04378253, -1.02646759, -1.00945504, -0.99272975,\n",
       "         -0.97627766, -0.96008565, -0.94414154, -0.92843389, -0.91295205,\n",
       "         -0.89768599, -0.88262633, -0.86776423, -0.85309137, -0.83859992,\n",
       "         -0.82428248, -0.81013204, -0.79614199, -0.78230606, -0.76861829,\n",
       "         -0.75507303, -0.74166492, -0.72838883, -0.7152399 , -0.70221349,\n",
       "         -0.68930516, -0.67651067, -0.66382599, -0.65124723, -0.63877068,\n",
       "         -0.62639278, -0.61411012, -0.60191941, -0.58981751, -0.57780139,\n",
       "         -0.56586812, -0.55401489, -0.542239  , -0.53053783, -0.51890885,\n",
       "         -0.50734962, -0.4958578 , -0.48443108, -0.47306728, -0.46176424,\n",
       "         -0.45051989, -0.43933221, -0.42819926, -0.41711913, -0.40608998,\n",
       "         -0.39511   , -0.38417746, -0.37329064, -0.36244788, -0.35164758,\n",
       "         -0.34088813, -0.33016801, -0.3194857 , -0.30883972, -0.29822863,\n",
       "         -0.28765101, -0.27710549, -0.26659069, -0.25610528, -0.24564796,\n",
       "         -0.23521743, -0.22481243, -0.21443171, -0.20407405, -0.19373823,\n",
       "         -0.18342307, -0.1731274 , -0.16285004, -0.15258985, -0.14234571,\n",
       "         -0.13211648, -0.12190105, -0.11169833, -0.10150723, -0.09132666,\n",
       "         -0.08115554, -0.07099282, -0.06083742, -0.05068829, -0.04054438,\n",
       "         -0.03040464, -0.02026802, -0.01013349,  0.        ,  0.01013349,\n",
       "          0.02026802,  0.03040464,  0.04054438,  0.05068829,  0.06083742,\n",
       "          0.07099282,  0.08115554,  0.09132666,  0.10150723,  0.11169833,\n",
       "          0.12190105,  0.13211648,  0.14234571,  0.15258985,  0.16285004,\n",
       "          0.1731274 ,  0.18342307,  0.19373823,  0.20407405,  0.21443171,\n",
       "          0.22481243,  0.23521743,  0.24564796,  0.25610528,  0.26659069,\n",
       "          0.27710549,  0.28765101,  0.29822863,  0.30883972,  0.3194857 ,\n",
       "          0.33016801,  0.34088813,  0.35164758,  0.36244788,  0.37329064,\n",
       "          0.38417746,  0.39511   ,  0.40608998,  0.41711913,  0.42819926,\n",
       "          0.43933221,  0.45051989,  0.46176424,  0.47306728,  0.48443108,\n",
       "          0.4958578 ,  0.50734962,  0.51890885,  0.53053783,  0.542239  ,\n",
       "          0.55401489,  0.56586812,  0.57780139,  0.58981751,  0.60191941,\n",
       "          0.61411012,  0.62639278,  0.63877068,  0.65124723,  0.66382599,\n",
       "          0.67651067,  0.68930516,  0.70221349,  0.7152399 ,  0.72838883,\n",
       "          0.74166492,  0.75507303,  0.76861829,  0.78230606,  0.79614199,\n",
       "          0.81013204,  0.82428248,  0.83859992,  0.85309137,  0.86776423,\n",
       "          0.88262633,  0.89768599,  0.91295205,  0.92843389,  0.94414154,\n",
       "          0.96008565,  0.97627766,  0.99272975,  1.00945504,  1.02646759,\n",
       "          1.04378253,  1.0614162 ,  1.07938624,  1.09771179,  1.11641358,\n",
       "          1.13551422,  1.15503839,  1.17501306,  1.1954679 ,  1.21643554,\n",
       "          1.23795207,  1.26005751,  1.28279645,  1.30621874,  1.33038042,\n",
       "          1.35534475,  1.38118357,  1.40797894,  1.43582519,  1.46483159,\n",
       "          1.49512565,  1.52685756,  1.56020597,  1.59538576,  1.63265879,\n",
       "          1.6723488 ,  1.71486302,  1.76072402,  1.81061863,  1.86547617,\n",
       "          1.92660022,  1.99590511,  2.07637768,  2.17308639,  2.29577765,\n",
       "          2.46756954,  2.77005632]),\n",
       "  array([  2860,   3600,   3900,   4620,   4700,   4730,   5000,   5070,\n",
       "           5300,   5580,   5720,   5940,   6120,   6300,   6400,   6490,\n",
       "          24570,  31350,  32280,  34160,  35300,  35860,  35900,  36720,\n",
       "          36740,  37280,  40260,  40700,  40810,  41580,  42680,  42700,\n",
       "          42700,  43280,  43700,  44200,  44440,  44730,  44880,  45120,\n",
       "          45540,  46200,  46800,  47400,  47630,  47700,  47700,  47760,\n",
       "          47790,  48950,  49100,  49950,  50050,  50300,  50380,  50400,\n",
       "          50800,  50800,  51370,  51390,  51810,  51900,  51920,  52400,\n",
       "          52650,  52700,  52800,  53100,  53100,  53280,  53280,  53400,\n",
       "          53460,  53600,  53600,  53640,  53730,  53820,  54200,  54240,\n",
       "          54360,  54400,  54810,  54960,  55000,  55000,  55000,  55170,\n",
       "          55200,  55200,  55400,  55400,  55440,  55440,  55660,  56160,\n",
       "          56430,  57240,  57690,  57860,  58160,  58300,  58500,  59000,\n",
       "          59100,  59130,  59400,  59400,  59400,  59670,  59800,  59900,\n",
       "          60170,  60190,  60200,  60320,  60390,  60500,  60600,  60750,\n",
       "          60940,  60940,  61050,  61290,  61380,  62800,  62880,  63120,\n",
       "          63250,  63400,  63570,  63580,  63600,  63800,  63840,  64000,\n",
       "          64100,  64100,  64200,  64300,  64350,  64800,  64800,  64890,\n",
       "          65520,  65560,  66480,  66600,  66780,  66880,  66900,  67140,\n",
       "          67300,  67770,  68200,  68200,  68240,  68310,  68520,  68750,\n",
       "          68760,  69000,  69080,  69200,  69480,  69680,  69930,  70000,\n",
       "          70200,  70290,  70400,  70400,  70590,  70600,  70800,  71190,\n",
       "          71280,  71500,  71520,  71610,  71610,  71680,  71760,  72200,\n",
       "          72400,  72930,  73260,  73700,  73920,  74200,  74280,  74360,\n",
       "          74400,  74690,  74700,  74800,  75400,  75400,  75400,  75570,\n",
       "          76010,  76230,  76400,  76560,  77000,  77330,  77660,  78100,\n",
       "          78600,  78650,  78980,  79800,  79800,  79970,  80740,  80850,\n",
       "          81070,  81240,  81360,  81840,  82170,  82320,  82610,  82800,\n",
       "          84100,  84480,  84500,  84590,  84920,  85900,  86130,  87890,\n",
       "          87960,  88660,  89700,  90860,  91520,  92730,  97080,  98160,\n",
       "          98280,  98340,  98670,  99320, 104610, 107900, 112320],\n",
       "        dtype=int64)),\n",
       " (20202.03758342947, 60302.10526315789, 0.9666457290290034))"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# probability plot\n",
    "stats.probplot(fraudY2.total_claim_amount, plot= plt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((array([-3.11449077e+00, -2.84275361e+00, -2.69067103e+00, -2.58319028e+00,\n",
       "         -2.49919966e+00, -2.42983495e+00, -2.37050124e+00, -2.31849806e+00,\n",
       "         -2.27209865e+00, -2.23012965e+00, -2.19175612e+00, -2.15636205e+00,\n",
       "         -2.12347952e+00, -2.09274444e+00, -2.06386774e+00, -2.03661596e+00,\n",
       "         -2.01079773e+00, -1.98625415e+00, -1.96285182e+00, -1.94047756e+00,\n",
       "         -1.91903454e+00, -1.89843922e+00, -1.87861902e+00, -1.85951048e+00,\n",
       "         -1.84105772e+00, -1.82321137e+00, -1.80592748e+00, -1.78916683e+00,\n",
       "         -1.77289422e+00, -1.75707796e+00, -1.74168942e+00, -1.72670259e+00,\n",
       "         -1.71209385e+00, -1.69784162e+00, -1.68392615e+00, -1.67032931e+00,\n",
       "         -1.65703445e+00, -1.64402618e+00, -1.63129030e+00, -1.61881366e+00,\n",
       "         -1.60658403e+00, -1.59459008e+00, -1.58282123e+00, -1.57126762e+00,\n",
       "         -1.55992001e+00, -1.54876980e+00, -1.53780888e+00, -1.52702966e+00,\n",
       "         -1.51642500e+00, -1.50598819e+00, -1.49571289e+00, -1.48559313e+00,\n",
       "         -1.47562326e+00, -1.46579794e+00, -1.45611212e+00, -1.44656102e+00,\n",
       "         -1.43714008e+00, -1.42784499e+00, -1.41867166e+00, -1.40961618e+00,\n",
       "         -1.40067483e+00, -1.39184409e+00, -1.38312057e+00, -1.37450105e+00,\n",
       "         -1.36598246e+00, -1.35756186e+00, -1.34923643e+00, -1.34100349e+00,\n",
       "         -1.33286044e+00, -1.32480484e+00, -1.31683430e+00, -1.30894655e+00,\n",
       "         -1.30113940e+00, -1.29341077e+00, -1.28575864e+00, -1.27818105e+00,\n",
       "         -1.27067616e+00, -1.26324217e+00, -1.25587733e+00, -1.24858000e+00,\n",
       "         -1.24134855e+00, -1.23418144e+00, -1.22707718e+00, -1.22003431e+00,\n",
       "         -1.21305144e+00, -1.20612723e+00, -1.19926037e+00, -1.19244959e+00,\n",
       "         -1.18569368e+00, -1.17899147e+00, -1.17234179e+00, -1.16574356e+00,\n",
       "         -1.15919569e+00, -1.15269715e+00, -1.14624693e+00, -1.13984405e+00,\n",
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       "          2.58319028e+00,  2.69067103e+00,  2.84275361e+00,  3.11449077e+00]),\n",
       "  array([   100,   1920,   2160,   2250,   2400,   2520,   2640,   2640,\n",
       "           2640,   2640,   2700,   2700,   2800,   2970,   3080,   3080,\n",
       "           3190,   3190,   3190,   3190,   3200,   3200,   3300,   3300,\n",
       "           3440,   3520,   3600,   3690,   3740,   3770,   3840,   3840,\n",
       "           3850,   3870,   3900,   3960,   3960,   4100,   4200,   4200,\n",
       "           4290,   4290,   4300,   4300,   4320,   4320,   4320,   4320,\n",
       "           4400,   4500,   4560,   4590,   4620,   4620,   4680,   4680,\n",
       "           4700,   4700,   4800,   4900,   4900,   4950,   4950,   4950,\n",
       "           5000,   5000,   5060,   5060,   5060,   5100,   5160,   5170,\n",
       "           5170,   5200,   5220,   5330,   5390,   5400,   5400,   5490,\n",
       "           5500,   5500,   5590,   5590,   5600,   5600,   5640,   5670,\n",
       "           5700,   5760,   5830,   5830,   5850,   5900,   5900,   5900,\n",
       "           5920,   5940,   5940,   5940,   6000,   6030,   6050,   6050,\n",
       "           6100,   6120,   6160,   6160,   6200,   6240,   6300,   6400,\n",
       "           6400,   6480,   6490,   6500,   6500,   6560,   6600,   6600,\n",
       "           6600,   6700,   6820,   6820,   6820,   6890,   6890,   6930,\n",
       "           6930,   7040,   7080,   7080,   7080,   7110,   7150,   7200,\n",
       "           7200,   7260,   7260,   7280,   7290,   7370,   7400,   7480,\n",
       "           7480,   7500,   7590,   7680,   7700,   7800,   8030,   8060,\n",
       "           8190,   8640,   8700,   8760,   8800,   8970,   9000,   9020,\n",
       "           9100,  10790,  18000,  19080,  24200,  26730,  27700,  28100,\n",
       "          28440,  28800,  29300,  29790,  30100,  30700,  30700,  31680,\n",
       "          31700,  32320,  32480,  32670,  32800,  33480,  33480,  33550,\n",
       "          33930,  34290,  34320,  34650,  34650,  34800,  35000,  35750,\n",
       "          36300,  36400,  36700,  36960,  37520,  37530,  37800,  37840,\n",
       "          38610,  38640,  38700,  38830,  39480,  39690,  39720,  39800,\n",
       "          40000,  40160,  40320,  40500,  40600,  40800,  41130,  41490,\n",
       "          41490,  41520,  41690,  41700,  41850,  42000,  42240,  42300,\n",
       "          42500,  42500,  42840,  42900,  42900,  42930,  43230,  43560,\n",
       "          43600,  44110,  44190,  44200,  44200,  44200,  44220,  44240,\n",
       "          44280,  44280,  44400,  44640,  44910,  45000,  45100,  45100,\n",
       "          45180,  45270,  45500,  45630,  45700,  46200,  46200,  46560,\n",
       "          46800,  46860,  46980,  46980,  47080,  47160,  47300,  47300,\n",
       "          47430,  47740,  47800,  48000,  48000,  48060,  48070,  48100,\n",
       "          48290,  48360,  48360,  48400,  48730,  48780,  48870,  48950,\n",
       "          49060,  49140,  49390,  49400,  49400,  49410,  49800,  49900,\n",
       "          50000,  50000,  50380,  50490,  50500,  50700,  50800,  51000,\n",
       "          51030,  51090,  51100,  51120,  51210,  51210,  51260,  51390,\n",
       "          51400,  51480,  51570,  51590,  51600,  51660,  51700,  51740,\n",
       "          51800,  51840,  52030,  52030,  52110,  52200,  52200,  52250,\n",
       "          52290,  52380,  52560,  52700,  52800,  52800,  53020,  53040,\n",
       "          53100,  53190,  53280,  53370,  53400,  53400,  53440,  53460,\n",
       "          53460,  53500,  53680,  53680,  53680,  53800,  53900,  54000,\n",
       "          54120,  54160,  54240,  54300,  54340,  54340,  54400,  54450,\n",
       "          54560,  54890,  54900,  55110,  55120,  55200,  55260,  55500,\n",
       "          55600,  55680,  55700,  55800,  55900,  56000,  56000,  56070,\n",
       "          56160,  56160,  56300,  56320,  56320,  56340,  56400,  56430,\n",
       "          56520,  56600,  56610,  57000,  57060,  57060,  57100,  57120,\n",
       "          57200,  57200,  57310,  57330,  57330,  57500,  57600,  57640,\n",
       "          57700,  57700,  57700,  57720,  57860,  57900,  57900,  57970,\n",
       "          58140,  58200,  58300,  58300,  58410,  58500,  58500,  58500,\n",
       "          58560,  58800,  58850,  58960,  59040,  59040,  59070,  59070,\n",
       "          59200,  59300,  59400,  59400,  59490,  59500,  59520,  59670,\n",
       "          59700,  59730,  59940,  60000,  60170,  60190,  60200,  60210,\n",
       "          60400,  60480,  60480,  60500,  60570,  60600,  60600,  60600,\n",
       "          60700,  60750,  60840,  61050,  61100,  61270,  61320,  61380,\n",
       "          61400,  61440,  61490,  61490,  61490,  61500,  61500,  61560,\n",
       "          61600,  61650,  61700,  61740,  61740,  61800,  61920,  62260,\n",
       "          62280,  62300,  62370,  62460,  62590,  62590,  62640,  62800,\n",
       "          62810,  62900,  62900,  62920,  62920,  62920,  63030,  63100,\n",
       "          63120,  63240,  63240,  63250,  63300,  63300,  63470,  63580,\n",
       "          63600,  63720,  63900,  63900,  63910,  64000,  64080,  64080,\n",
       "          64080,  64100,  64200,  64240,  64260,  64320,  64350,  64350,\n",
       "          64400,  64400,  64570,  64620,  64680,  64800,  64900,  64920,\n",
       "          65040,  65070,  65100,  65250,  65400,  65430,  65440,  65500,\n",
       "          65520,  65780,  65780,  65790,  65800,  66200,  66200,  66240,\n",
       "          66550,  66550,  66660,  66660,  66780,  66840,  66950,  66950,\n",
       "          67200,  67210,  67320,  67320,  67500,  67600,  67650,  67800,\n",
       "          67800,  68000,  68040,  68090,  68160,  68300,  68400,  68530,\n",
       "          68580,  68750,  68760,  68970,  69100,  69300,  69300,  69300,\n",
       "          69360,  69400,  69400,  69480,  69480,  69630,  69700,  69740,\n",
       "          69840,  69850,  70290,  70290,  70290,  70400,  70400,  70500,\n",
       "          70510,  70680,  70700,  70830,  70900,  70900,  70920,  71060,\n",
       "          71100,  71440,  71640,  71800,  72000,  72100,  72120,  72800,\n",
       "          72820,  72840,  72900,  72930,  73320,  73370,  73400,  73500,\n",
       "          73560,  73800,  74030,  74140,  74140,  74160,  74200,  74200,\n",
       "          74360,  74700,  74700,  74880,  74900,  75400,  75460,  75500,\n",
       "          75600,  75690,  75790,  75960,  76050,  76120,  76120,  76400,\n",
       "          76450,  76560,  76600,  76700,  76890,  76900,  76920,  77000,\n",
       "          77040,  77100,  77100,  77110,  77110,  77130,  77200,  77440,\n",
       "          77440,  77440,  77700,  77770,  77800,  77880,  77880,  77880,\n",
       "          77990,  78000,  78120,  78200,  78240,  78300,  78320,  78500,\n",
       "          78650,  78870,  78900,  79080,  79090,  79090,  79300,  79320,\n",
       "          79500,  79500,  79530,  79560,  79560,  79600,  79680,  79750,\n",
       "          79800,  80080,  80100,  80280,  80520,  80880,  80960,  81070,\n",
       "          81120,  81400,  81500,  81800,  81960,  82060,  82170,  82400,\n",
       "          82720,  82830,  83160,  83160,  83490,  84500,  84590,  84590,\n",
       "          84600,  84720,  85020,  85150,  85250,  85300,  85320,  85690,\n",
       "          86060,  86130,  86400,  86790,  87010,  87100,  87200,  87300,\n",
       "          87780,  87900,  88110,  88220,  88400,  88920,  89400,  89520,\n",
       "          89650,  90000,  90240,  90400,  90480,  90530,  90600,  90970,\n",
       "          91080,  91260,  91650,  93480,  93720,  93730,  94560,  94930,\n",
       "          95000,  95150,  95810,  95900,  97080,  99990, 100210, 100800,\n",
       "         101010, 101860, 103560, 105040, 105820, 108030, 108480, 114920],\n",
       "        dtype=int64)),\n",
       " (26445.203455495135, 50230.265957446805, 0.9572168988237284))"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# probability plot\n",
    "stats.probplot(fraudN2.total_claim_amount, plot= plt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Correlation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>months_bf_incident</th>\n",
       "      <th>total_claim_amount</th>\n",
       "      <th>witnesses</th>\n",
       "      <th>policy_deductable</th>\n",
       "      <th>umbrella_limit</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>months_bf_incident</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.002242</td>\n",
       "      <td>-0.056202</td>\n",
       "      <td>0.051403</td>\n",
       "      <td>-0.045374</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>total_claim_amount</th>\n",
       "      <td>-0.002242</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.010440</td>\n",
       "      <td>0.024516</td>\n",
       "      <td>-0.038972</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>witnesses</th>\n",
       "      <td>-0.056202</td>\n",
       "      <td>-0.010440</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.066224</td>\n",
       "      <td>-0.007144</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>policy_deductable</th>\n",
       "      <td>0.051403</td>\n",
       "      <td>0.024516</td>\n",
       "      <td>0.066224</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.009927</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>umbrella_limit</th>\n",
       "      <td>-0.045374</td>\n",
       "      <td>-0.038972</td>\n",
       "      <td>-0.007144</td>\n",
       "      <td>0.009927</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                    months_bf_incident  total_claim_amount  witnesses  \\\n",
       "months_bf_incident            1.000000           -0.002242  -0.056202   \n",
       "total_claim_amount           -0.002242            1.000000  -0.010440   \n",
       "witnesses                    -0.056202           -0.010440   1.000000   \n",
       "policy_deductable             0.051403            0.024516   0.066224   \n",
       "umbrella_limit               -0.045374           -0.038972  -0.007144   \n",
       "\n",
       "                    policy_deductable  umbrella_limit  \n",
       "months_bf_incident           0.051403       -0.045374  \n",
       "total_claim_amount           0.024516       -0.038972  \n",
       "witnesses                    0.066224       -0.007144  \n",
       "policy_deductable            1.000000        0.009927  \n",
       "umbrella_limit               0.009927        1.000000  "
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create new dataset with quantitative variables - full dataframe\n",
    "dfClaims_quant = dfClaims.filter(['months_bf_incident', 'total_claim_amount', 'witnesses', 'policy_deductable', 'umbrella_limit'], axis=1)\n",
    "dfClaims_quant.corr()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>months_bf_incident</th>\n",
       "      <th>total_claim_amount</th>\n",
       "      <th>witnesses</th>\n",
       "      <th>policy_deductable</th>\n",
       "      <th>umbrella_limit</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>months_bf_incident</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.132688</td>\n",
       "      <td>-0.080317</td>\n",
       "      <td>0.002766</td>\n",
       "      <td>0.006353</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>total_claim_amount</th>\n",
       "      <td>0.132688</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.037589</td>\n",
       "      <td>-0.104484</td>\n",
       "      <td>-0.022993</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>witnesses</th>\n",
       "      <td>-0.080317</td>\n",
       "      <td>0.037589</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.031163</td>\n",
       "      <td>-0.037245</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>policy_deductable</th>\n",
       "      <td>0.002766</td>\n",
       "      <td>-0.104484</td>\n",
       "      <td>0.031163</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.011936</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>umbrella_limit</th>\n",
       "      <td>0.006353</td>\n",
       "      <td>-0.022993</td>\n",
       "      <td>-0.037245</td>\n",
       "      <td>-0.011936</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                    months_bf_incident  total_claim_amount  witnesses  \\\n",
       "months_bf_incident            1.000000            0.132688  -0.080317   \n",
       "total_claim_amount            0.132688            1.000000   0.037589   \n",
       "witnesses                    -0.080317            0.037589   1.000000   \n",
       "policy_deductable             0.002766           -0.104484   0.031163   \n",
       "umbrella_limit                0.006353           -0.022993  -0.037245   \n",
       "\n",
       "                    policy_deductable  umbrella_limit  \n",
       "months_bf_incident           0.002766        0.006353  \n",
       "total_claim_amount          -0.104484       -0.022993  \n",
       "witnesses                    0.031163       -0.037245  \n",
       "policy_deductable            1.000000       -0.011936  \n",
       "umbrella_limit              -0.011936        1.000000  "
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create new dataset with quantitative variables - full dataframe\n",
    "fraudY2_quant = fraudY2.filter(['months_bf_incident', 'total_claim_amount', 'witnesses', 'policy_deductable', 'umbrella_limit'], axis=1)\n",
    "fraudY2_quant.corr()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>months_bf_incident</th>\n",
       "      <th>total_claim_amount</th>\n",
       "      <th>witnesses</th>\n",
       "      <th>policy_deductable</th>\n",
       "      <th>umbrella_limit</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>months_bf_incident</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.035670</td>\n",
       "      <td>-0.048958</td>\n",
       "      <td>0.067778</td>\n",
       "      <td>-0.064554</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>total_claim_amount</th>\n",
       "      <td>-0.035670</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.032133</td>\n",
       "      <td>0.055139</td>\n",
       "      <td>-0.057434</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>witnesses</th>\n",
       "      <td>-0.048958</td>\n",
       "      <td>-0.032133</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.076749</td>\n",
       "      <td>-0.000597</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>policy_deductable</th>\n",
       "      <td>0.067778</td>\n",
       "      <td>0.055139</td>\n",
       "      <td>0.076749</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.017126</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>umbrella_limit</th>\n",
       "      <td>-0.064554</td>\n",
       "      <td>-0.057434</td>\n",
       "      <td>-0.000597</td>\n",
       "      <td>0.017126</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                    months_bf_incident  total_claim_amount  witnesses  \\\n",
       "months_bf_incident            1.000000           -0.035670  -0.048958   \n",
       "total_claim_amount           -0.035670            1.000000  -0.032133   \n",
       "witnesses                    -0.048958           -0.032133   1.000000   \n",
       "policy_deductable             0.067778            0.055139   0.076749   \n",
       "umbrella_limit               -0.064554           -0.057434  -0.000597   \n",
       "\n",
       "                    policy_deductable  umbrella_limit  \n",
       "months_bf_incident           0.067778       -0.064554  \n",
       "total_claim_amount           0.055139       -0.057434  \n",
       "witnesses                    0.076749       -0.000597  \n",
       "policy_deductable            1.000000        0.017126  \n",
       "umbrella_limit               0.017126        1.000000  "
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create new dataset with quantitative variables - full dataframe\n",
    "fraudN2_quant = fraudN2.filter(['months_bf_incident', 'total_claim_amount', 'witnesses', 'policy_deductable', 'umbrella_limit'], axis=1)\n",
    "fraudN2_quant.corr()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Point Piserial Correlation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Point-biserial correlation is used for correlation between the binary fraud reported variable and continuous variables. None of the point-biserial correlations for the fraud_reported feature are strong. However, the p-value for umbrella limit shows that it may be significant."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PointbiserialrResult(correlation=-0.16478101492025085, pvalue=1.627232492099993e-07)"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pbc = stats.pointbiserialr(dfClaims.fraud_reported_f, dfClaims.total_claim_amount)\n",
    "pbc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PointbiserialrResult(correlation=-0.05813100524817261, pvalue=0.06626935848682936)"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pbc = stats.pointbiserialr(dfClaims.fraud_reported_f, dfClaims.umbrella_limit)\n",
    "pbc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PointbiserialrResult(correlation=-0.0014579814179212156, pvalue=0.9632905687387004)"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pbc = stats.pointbiserialr(dfClaims.fraud_reported_f, dfClaims.months_bf_incident)\n",
    "pbc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PointbiserialrResult(correlation=-0.04925815127227322, pvalue=0.11973286668807653)"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pbc = stats.pointbiserialr(dfClaims.fraud_reported_f, dfClaims.witnesses)\n",
    "pbc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PointbiserialrResult(correlation=-0.014231171157091445, pvalue=0.6532414524704065)"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pbc = stats.pointbiserialr(dfClaims.fraud_reported_f, dfClaims.policy_deductable)\n",
    "pbc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Hypothesis Testing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Difference in Means Hypothesis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> **There is no difference in the means of variables in the fraud reported subset and the same variables in the fraud not reported subset.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.076"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# To compute the p-value of an observed difference in means, we can assume that there is no difference between the groups and \n",
    "# generate simulated results by shuffling the data\n",
    "\n",
    "class DiffMeansPermute(thinkstats2.HypothesisTest):\n",
    "\n",
    "    def TestStatistic(self, data):\n",
    "        group1, group2 = data\n",
    "        test_stat = abs(group1.mean() - group2.mean())\n",
    "        return test_stat\n",
    "\n",
    "    def MakeModel(self):\n",
    "        group1, group2 = self.data\n",
    "        self.n, self.m = len(group1), len(group2)\n",
    "        self.pool = np.hstack((group1, group2))\n",
    "\n",
    "    def RunModel(self):\n",
    "        np.random.shuffle(self.pool)\n",
    "        data = self.pool[:self.n], self.pool[self.n:]\n",
    "        return data\n",
    "    \n",
    "data = fraudY2['umbrella_limit'], fraudN2['umbrella_limit']\n",
    "ht = DiffMeansPermute(data)\n",
    "pvalue = ht.PValue(iters=1000)\n",
    "pvalue"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.662"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# To compute the p-value of an observed difference in means, we can assume that there is no difference between the groups and \n",
    "# generate simulated results by shuffling the data\n",
    "\n",
    "class DiffMeansPermute(thinkstats2.HypothesisTest):\n",
    "\n",
    "    def TestStatistic(self, data):\n",
    "        group1, group2 = data\n",
    "        test_stat = abs(group1.mean() - group2.mean())\n",
    "        return test_stat\n",
    "\n",
    "    def MakeModel(self):\n",
    "        group1, group2 = self.data\n",
    "        self.n, self.m = len(group1), len(group2)\n",
    "        self.pool = np.hstack((group1, group2))\n",
    "\n",
    "    def RunModel(self):\n",
    "        np.random.shuffle(self.pool)\n",
    "        data = self.pool[:self.n], self.pool[self.n:]\n",
    "        return data\n",
    "    \n",
    "data = fraudY2['policy_deductable'], fraudN2['policy_deductable']\n",
    "ht = DiffMeansPermute(data)\n",
    "pvalue = ht.PValue(iters=1000)\n",
    "pvalue"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# To compute the p-value of an observed difference in means, we can assume that there is no difference between the groups and \n",
    "# generate simulated results by shuffling the data\n",
    "\n",
    "class DiffMeansPermute(thinkstats2.HypothesisTest):\n",
    "\n",
    "    def TestStatistic(self, data):\n",
    "        group1, group2 = data\n",
    "        test_stat = abs(group1.mean() - group2.mean())\n",
    "        return test_stat\n",
    "\n",
    "    def MakeModel(self):\n",
    "        group1, group2 = self.data\n",
    "        self.n, self.m = len(group1), len(group2)\n",
    "        self.pool = np.hstack((group1, group2))\n",
    "\n",
    "    def RunModel(self):\n",
    "        np.random.shuffle(self.pool)\n",
    "        data = self.pool[:self.n], self.pool[self.n:]\n",
    "        return data\n",
    "    \n",
    "data = fraudY2['total_claim_amount'], fraudN2['total_claim_amount']\n",
    "ht = DiffMeansPermute(data)\n",
    "pvalue = ht.PValue(iters=1000)\n",
    "pvalue"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.958"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# To compute the p-value of an observed difference in means, we can assume that there is no difference between the groups and \n",
    "# generate simulated results by shuffling the data\n",
    "\n",
    "class DiffMeansPermute(thinkstats2.HypothesisTest):\n",
    "\n",
    "    def TestStatistic(self, data):\n",
    "        group1, group2 = data\n",
    "        test_stat = abs(group1.mean() - group2.mean())\n",
    "        return test_stat\n",
    "\n",
    "    def MakeModel(self):\n",
    "        group1, group2 = self.data\n",
    "        self.n, self.m = len(group1), len(group2)\n",
    "        self.pool = np.hstack((group1, group2))\n",
    "\n",
    "    def RunModel(self):\n",
    "        np.random.shuffle(self.pool)\n",
    "        data = self.pool[:self.n], self.pool[self.n:]\n",
    "        return data\n",
    "    \n",
    "data = fraudY2['months_bf_incident'], fraudN2['months_bf_incident']\n",
    "ht = DiffMeansPermute(data)\n",
    "pvalue = ht.PValue(iters=1000)\n",
    "pvalue"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.13"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# To compute the p-value of an observed difference in means, we can assume that there is no difference between the groups and \n",
    "# generate simulated results by shuffling the data\n",
    "\n",
    "class DiffMeansPermute(thinkstats2.HypothesisTest):\n",
    "\n",
    "    def TestStatistic(self, data):\n",
    "        group1, group2 = data\n",
    "        test_stat = abs(group1.mean() - group2.mean())\n",
    "        return test_stat\n",
    "\n",
    "    def MakeModel(self):\n",
    "        group1, group2 = self.data\n",
    "        self.n, self.m = len(group1), len(group2)\n",
    "        self.pool = np.hstack((group1, group2))\n",
    "\n",
    "    def RunModel(self):\n",
    "        np.random.shuffle(self.pool)\n",
    "        data = self.pool[:self.n], self.pool[self.n:]\n",
    "        return data\n",
    "    \n",
    "data = fraudY2['witnesses'], fraudN2['witnesses']\n",
    "ht = DiffMeansPermute(data)\n",
    "pvalue = ht.PValue(iters=1000)\n",
    "pvalue"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Correlation Hypothesis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> **There is no significant linear relationship between the fraud reported target variable and any of the claim transaction variables.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.966"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Testing correlation\n",
    "#stats.pointbiserialr()\n",
    "# To check whether an observed correlation is statistically significant, we can run a permutation test \n",
    "class CorrelationPermute(thinkstats2.HypothesisTest):\n",
    "\n",
    "    def TestStatistic(self, data):\n",
    "        xs, ys = data\n",
    "        test_stat = stats.pointbiserialr(xs, ys)\n",
    "        return test_stat[0]\n",
    "\n",
    "    def RunModel(self):\n",
    "        xs, ys = self.data\n",
    "        xs = np.random.permutation(xs)\n",
    "        return xs, ys\n",
    "\n",
    "data = dfClaims['fraud_reported_f'], dfClaims['umbrella_limit']\n",
    "ht = CorrelationPermute(data)\n",
    "pvalue = ht.PValue(iters=1000)\n",
    "pvalue"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Testing correlation\n",
    "#stats.pointbiserialr()\n",
    "# To check whether an observed correlation is statistically significant, we can run a permutation test \n",
    "class CorrelationPermute(thinkstats2.HypothesisTest):\n",
    "\n",
    "    def TestStatistic(self, data):\n",
    "        xs, ys = data\n",
    "        test_stat = stats.pointbiserialr(xs, ys)\n",
    "        return test_stat[0]\n",
    "\n",
    "    def RunModel(self):\n",
    "        xs, ys = self.data\n",
    "        xs = np.random.permutation(xs)\n",
    "        return xs, ys\n",
    "\n",
    "data = dfClaims['fraud_reported_f'], dfClaims['total_claim_amount']\n",
    "ht = CorrelationPermute(data)\n",
    "pvalue = ht.PValue(iters=1000)\n",
    "pvalue"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.523"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#stats.pointbiserialr()\n",
    "# To check whether an observed correlation is statistically significant, we can run a permutation test \n",
    "class CorrelationPermute(thinkstats2.HypothesisTest):\n",
    "\n",
    "    def TestStatistic(self, data):\n",
    "        xs, ys = data\n",
    "        test_stat = stats.pointbiserialr(xs, ys)\n",
    "        return test_stat[0]\n",
    "\n",
    "    def RunModel(self):\n",
    "        xs, ys = self.data\n",
    "        xs = np.random.permutation(xs)\n",
    "        return xs, ys\n",
    "\n",
    "data = dfClaims['fraud_reported_f'], dfClaims['months_bf_incident']\n",
    "ht = CorrelationPermute(data)\n",
    "pvalue = ht.PValue(iters=1000)\n",
    "pvalue"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.953"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#stats.pointbiserialr()\n",
    "# To check whether an observed correlation is statistically significant, we can run a permutation test \n",
    "class CorrelationPermute(thinkstats2.HypothesisTest):\n",
    "\n",
    "    def TestStatistic(self, data):\n",
    "        xs, ys = data\n",
    "        test_stat = stats.pointbiserialr(xs, ys)\n",
    "        return test_stat[0]\n",
    "\n",
    "    def RunModel(self):\n",
    "        xs, ys = self.data\n",
    "        xs = np.random.permutation(xs)\n",
    "        return xs, ys\n",
    "\n",
    "data = dfClaims['fraud_reported_f'], dfClaims['witnesses']\n",
    "ht = CorrelationPermute(data)\n",
    "pvalue = ht.PValue(iters=1000)\n",
    "pvalue"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.685"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#stats.pointbiserialr()\n",
    "# To check whether an observed correlation is statistically significant, we can run a permutation test \n",
    "class CorrelationPermute(thinkstats2.HypothesisTest):\n",
    "\n",
    "    def TestStatistic(self, data):\n",
    "        xs, ys = data\n",
    "        test_stat = stats.pointbiserialr(xs, ys)\n",
    "        return test_stat[0]\n",
    "\n",
    "    def RunModel(self):\n",
    "        xs, ys = self.data\n",
    "        xs = np.random.permutation(xs)\n",
    "        return xs, ys\n",
    "\n",
    "data = dfClaims['fraud_reported_f'], dfClaims['policy_deductable']\n",
    "ht = CorrelationPermute(data)\n",
    "pvalue = ht.PValue(iters=1000)\n",
    "pvalue"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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