DS_L4_22_Apr_Assignment.ipynb

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    "colab": {
      "name": "DS_L4_22_Apr_Assignment.ipynb",
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      "include_colab_link": true
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    "kernelspec": {
      "display_name": "Python 3",
      "language": "python",
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      "file_extension": ".py",
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      "pygments_lexer": "ipython3",
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  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/chindimaga/SHALA2020/blob/master/DS_L4_22_Apr_Assignment.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "NVMUAJt8gzbA"
      },
      "source": [
        "# MLE and Hypothesis Testing"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "d1-kEc8hXx3N"
      },
      "source": [
        "### Read the given csv file [```q4.csv```](https://raw.githubusercontent.com/Ipsit1234/SHALA/master/q4.csv) of samples. Assume that it is drawn from a exponential distribution. What is the difference of log likelihoods for $\\lambda = 1$ and $\\lambda = 2$ ? Which of the two is more strongly supported?"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "DHfUkvD3KcNN",
        "colab": {}
      },
      "source": [
        "import numpy as np\n",
        "import pandas as pd\n",
        "from scipy import stats\n",
        "from matplotlib import pyplot as plt\n",
        "import seaborn as sns"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "UAphR126LEwa",
        "colab": {},
        "outputId": "03234afb-76ed-4125-e93e-2b6e3d28070b"
      },
      "source": [
        "url = 'https://raw.githubusercontent.com/Ipsit1234/SHALA/master/q4.csv'\n",
        "data = pd.read_csv(url,header=None)\n",
        "data.head()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
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              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>0</th>\n",
              "      <th>1</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>0</td>\n",
              "      <td>0.019404</td>\n",
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              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>1</td>\n",
              "      <td>0.043634</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>2</td>\n",
              "      <td>0.023797</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>3</td>\n",
              "      <td>0.444340</td>\n",
              "    </tr>\n",
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              "      <th>4</th>\n",
              "      <td>4</td>\n",
              "      <td>0.578160</td>\n",
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            "text/plain": [
              "   0         1\n",
              "0  0  0.019404\n",
              "1  1  0.043634\n",
              "2  2  0.023797\n",
              "3  3  0.444340\n",
              "4  4  0.578160"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 2
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "nDpo9jpidQHk"
      },
      "source": [
        "# PDF of exponential distribution is $\\lambda e^{-\\lambda x}$\n",
        "Define a function to find pdf. You can use any module to get pre-defined functions also. And then find the likelihood and log-likelihood"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "Hio8uXrtLjl7",
        "colab": {},
        "outputId": "91f8929a-04eb-4192-c93a-5a03df05e710"
      },
      "source": [
        "def pdf_exp(lam,x):\n",
        "    return lam * np.exp(-1*lam*x)\n",
        "\n",
        "likelihood_1 = np.prod(pdf_exp(1,data[1].values))\n",
        "likelihood_2 = np.prod(pdf_exp(2,data[1].values))\n",
        "\n",
        "log_likelihood_1 = np.log(likelihood_1)\n",
        "log_likelihood_2 = np.log(likelihood_2)\n",
        "\n",
        "print(\"When lambda = 1, likelihood is {} and log-likelihood is {}\".format(likelihood_1,log_likelihood_1))\n",
        "print(\"When lambda = 2, likelihood is {} and log-likelihood is {}\".format(likelihood_2,log_likelihood_2))"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "When lambda = 1, likelihood is 5.52106601597132e-22 and log-likelihood is -48.94830108538966\n",
            "When lambda = 2, likelihood is 3.864074103681613e-13 and log-likelihood is -28.581884114784785\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "q214ixOGeR35"
      },
      "source": [
        "### Read the csv files [```q4_1.csv```](https://raw.githubusercontent.com/Ipsit1234/SHALA/master/q4_1.csv) and [```q4_2.csv```](https://raw.githubusercontent.com/Ipsit1234/SHALA/master/q4_2.csv) to get samples from two unknown distributions. Choose a significance level and implement the the most general two-sample t-test"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "bAsMqWiGdb52",
        "colab": {}
      },
      "source": [
        "sample1 = pd.read_csv('https://raw.githubusercontent.com/Ipsit1234/SHALA/master/q4_1.csv',header=None)\n",
        "sample2 = pd.read_csv('https://raw.githubusercontent.com/Ipsit1234/SHALA/master/q4_2.csv',header=None)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "yIvOH3yWiTU9"
      },
      "source": [
        "Find the parameters required to compute the T statistic"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "_3TBrHZifG2u",
        "colab": {}
      },
      "source": [
        "significance = 0.05\n",
        "mu1 = np.mean(sample1[1].values)\n",
        "s1 = np.var(sample1[1].values)\n",
        "n1 = sample1[1].shape[0]\n",
        "mu2 = np.mean(sample2[1].values)\n",
        "s2 = np.var(sample2[1].values)\n",
        "n2 = sample2[1].shape[0]"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "3i3gxyQziXD5"
      },
      "source": [
        "Find the degrees of freedom to get the critical value"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "p4Hx9UL3flF8",
        "colab": {}
      },
      "source": [
        "df = np.square((s1**2)/n1 +(s2**2)/n2)/((((s1**2)/n1)**2)/(n1-1)+(((s1**2)/n1)**2)/(n2-1))"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "nyai_S1zihfm"
      },
      "source": [
        "Compare the critical value and the T statistic and conclude whether null hypothesis is accepted or not. Print 'YES' is it is rejected, otherwise print 'NO'."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "ST8J42mAfn0R",
        "colab": {},
        "outputId": "4f791372-bc34-430e-a26d-62ed21163182"
      },
      "source": [
        "T = (mu1 - mu2)/np.sqrt(s1/n1 +s2/n2)\n",
        "critical = stats.t.pdf(1-significance/2,df)\n",
        "if np.abs(T) > critical:\n",
        "    print('YES')\n",
        "else:\n",
        "    print('NO')"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "YES\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "SrOP9BwSiwVc"
      },
      "source": [
        "Plot the distribution of both the samples to visualize"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "omfVDZqxfyAM",
        "outputId": "46dece49-758d-4830-9865-976145d664f3",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        }
      },
      "source": [
        "sns.distplot(sample1[1].values)\n",
        "\n",
        "sns.distplot(sample2[1].values)\n",
        "plt.legend(['first sample','second sample'])\n",
        "plt.show()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}