Lecture05.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: mean, standard deviation of a sample"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 187.05428407  204.35972329  179.58852556  166.74574824  233.98637717\n",
      "  226.25311383  176.23823665  211.36339224  173.35166339  191.17625306]\n",
      "Mean =   200\n",
      "Median =   200\n",
      "Mode =   203\n",
      "Standard deviation =  25.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11fc42c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# standard preamble\n",
    "import numpy as np\n",
    "import scipy as sp\n",
    "from scipy import stats\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "# create a set of data and compute mean and variance\n",
    "# This creates an array of 100 elements, \n",
    "# gaussian-distributed with mean of 200 and RMS of 25\n",
    "mu = 200\n",
    "sigma = 25\n",
    "x = mu + sigma*np.random.randn(10000000)\n",
    "print x[0:10]\n",
    "n, bins, patches = plt.hist(x, 20, normed=True)\n",
    "\n",
    "# various measures of \"average value\":\n",
    "print 'Mean = {0:5.0f}'.format(sp.mean(x))\n",
    "print 'Median = {0:5.0f}'.format(sp.median(x))\n",
    "print 'Mode = {0:5.0f}'.format(0.5*(bins[np.argmax(n)]+bins[np.argmax(n)+1]))\n",
    "\n",
    "# measure of the spreadx\n",
    "print 'Standard deviation = {0:5.1f}'.format(np.std(x))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Fitting\n",
    "\n",
    "The simplest technique to describe is least-squares fitting (see lecture notes). Usually you use the least-squares fit if you have a graph (i.e. a set of data points $y_i(x_i)$), you want to describe it in terms of a model $y(x;\\theta)$, where parameters $\\theta$ are unknown. You fit to determine the values of $\\theta$ and (hopefully) their uncertainties.  \n",
    "\n",
    "There are two standard cases where least-squares method is applicable:\n",
    "1. You know errors for each data point $\\sigma_i$ and you know that those errors are Gaussian. In this case, you minimize $\\chi^2=\\sum \\left(\\frac{y_i - y(x_i;\\theta)}{\\sigma_i}\\right)^2$. The value of the $\\chi^2_{\\min}$ can be interpreted as a goodness-of-fit, and the errors on parameters $\\theta$ have probabilistic interpretation\n",
    "1. You know that the errors are Gaussian and are the same for each data point, but you do not know their magnitude. In this case, you would minimize the sum of squares: $\\mathcal{S} = \\sum \\left(y_i - y(x_i;\\theta)\\right)^2$. In this case the value of $\\mathcal{S}$ can be used to compute the errors $\\sigma_i$ for each data point, and the errors on $\\theta$ have probabilistic definition, but you lose information about the goodness of fit\n",
    "1. If the errors are not known to be Gaussian, then the least square method is not useful to estimate uncertainties or the goodness of fit. It is also not guaranteed to be unbiased or most efficient. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### Examples"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Polynomial fit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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HbFLSS9tuv6zEwiQXtq+WdL2kJ6qtpDftNsXTkl6V1IiIlI5yvyzpi2pdV5KqkLRi+0nb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\nc3gAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1258a2310>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.optimize as fitter\n",
    "\n",
    "\n",
    "# Generate artificial data = straight line with a=0 and b=1\n",
    "# plus some noise.\n",
    "a0 = 0\n",
    "b0 = 1\n",
    "xdata = np.array([0.0,1.0,2.0,3.0,4.0,5.0])\n",
    "ydata = np.array([0.1,0.9,2.2,2.8,3.9,3.1])\n",
    "sigma = np.array([1.0,1.0,1.0,1.0,1.0,1.0])\n",
    "\n",
    "# plot it\n",
    "plt.errorbar(xdata, ydata, xerr=0, yerr=sigma, fmt='o')\n",
    "plt.xlim(-1,6)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now define a the model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# linear function\n",
    "def model(x, a, b):\n",
    "    return a + b*x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The fitter needs a good initial guess of parameters (more on that later):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.40952381  0.70285714]\n",
      "[[ 0.19750113 -0.05386395]\n",
      " [-0.05386395  0.02154558]]\n",
      "a= 0.410+/-0.444\n",
      "b= 0.703+/-0.147\n",
      "[[ 1.         -0.82572283]\n",
      " [-0.82572283  1.        ]]\n",
      "chi^2 =  1.51\n",
      "chi^2/d.f.= 0.38\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1258a2590>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Initial guess.\n",
    "par0    = np.array([0.0, 1.0])\n",
    "par, cov = fitter.curve_fit(model, xdata, ydata, p0=par0, sigma=sigma)\n",
    "print par\n",
    "print cov\n",
    "\n",
    "# decode it now\n",
    "print 'a={0:6.3f}+/-{1:5.3f}'.format(par[0],np.sqrt(cov[0,0]))\n",
    "print 'b={0:6.3f}+/-{1:5.3f}'.format(par[1],np.sqrt(cov[1,1]))\n",
    "\n",
    "corr = cov.copy() # copy shape\n",
    "# compute correlation matrix\n",
    "for i in range(len(par)):\n",
    "    for j in range(len(par)):\n",
    "        corr[i,j] = cov[i,j]/np.sqrt(cov[i,i]*cov[j,j])\n",
    "        \n",
    "print corr\n",
    "\n",
    "# compute reduced chi2\n",
    "chi_squared = np.sum(((model(xdata, *par)-ydata)/sigma)**2)\n",
    "reduced_chi_squared = (chi_squared)/(len(xdata)-len(par))\n",
    "print 'chi^2 = {0:5.2f}'.format(chi_squared)\n",
    "print 'chi^2/d.f.={0:5.2f}'.format(reduced_chi_isquared)\n",
    "\n",
    "# overlay plot over data\n",
    "plt.errorbar(xdata, ydata, xerr=0, yerr=sigma, fmt='o')\n",
    "plt.xlim(-1,6)\n",
    "xfit = np.linspace(0,5,50)\n",
    "plt.plot(xfit,model(xfit,par[0],par[1]),'r-')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-0.11428571  1.48857143 -0.15714286]\n",
      "[[ 0.16053059 -0.11516325  0.01744898]\n",
      " [-0.11516325  0.14203469 -0.02617347]\n",
      " [ 0.01744898 -0.02617347  0.00523469]]\n",
      "a=-0.114+/-0.401\n",
      "b= 1.489+/-0.377\n",
      "c=-0.157+/-0.072\n",
      "[[ 1.         -0.76267202  0.60192927]\n",
      " [-0.76267202  1.         -0.95988329]\n",
      " [ 0.60192927 -0.95988329  1.        ]]\n",
      "chi^2 =  0.59\n",
      "chi^2/d.f.= 0.20\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x115ca4090>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from numpy import sqrt\n",
    "\n",
    "# quadratic function\n",
    "def model2(x, a, b, c):\n",
    "    return a + b*x + c*x*x\n",
    "\n",
    "par0    = np.array([0.0, 1.0, 0.0])\n",
    "par, cov = fitter.curve_fit(model2, xdata, ydata, par0, sigma)\n",
    "print par\n",
    "print cov\n",
    "\n",
    "# decode it now\n",
    "print 'a={0:6.3f}+/-{1:5.3f}'.format(par[0],sqrt(cov[0,0]))\n",
    "print 'b={0:6.3f}+/-{1:5.3f}'.format(par[1],sqrt(cov[1,1]))\n",
    "print 'c={0:6.3f}+/-{1:5.3f}'.format(par[2],sqrt(cov[2,2]))\n",
    "\n",
    "corr = cov.copy() # copy shape\n",
    "# compute correlation matrix\n",
    "for i in range(len(par)):\n",
    "    for j in range(len(par)):\n",
    "        corr[i,j] = cov[i,j]/sqrt(cov[i,i]*cov[j,j])\n",
    "        \n",
    "print corr\n",
    "\n",
    "# compute reduced chi2\n",
    "chi_squared = np.sum(((model2(xdata, *par)-ydata)/sigma)**2)\n",
    "reduced_chi_squared = (chi_squared)/(len(xdata)-len(par))\n",
    "print 'chi^2 = {0:5.2f}'.format(chi_squared)\n",
    "print 'chi^2/d.f.={0:5.2f}'.format(reduced_chi_squared)\n",
    "\n",
    "# overlay plot over data\n",
    "plt.errorbar(xdata, ydata, xerr=0, yerr=sigma, fmt='o')\n",
    "plt.xlim(-1,6)\n",
    "xfit = np.linspace(0,5,50)\n",
    "plt.plot(xfit,model2(xfit,par[0],par[1], par[2]),'r-')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.1  -1.65  4.45 -2.55  0.6  -0.05]\n",
      "[[ inf  inf  inf  inf  inf  inf]\n",
      " [ inf  inf  inf  inf  inf  inf]\n",
      " [ inf  inf  inf  inf  inf  inf]\n",
      " [ inf  inf  inf  inf  inf  inf]\n",
      " [ inf  inf  inf  inf  inf  inf]\n",
      " [ inf  inf  inf  inf  inf  inf]]\n",
      "[[ nan  nan  nan  nan  nan  nan]\n",
      " [ nan  nan  nan  nan  nan  nan]\n",
      " [ nan  nan  nan  nan  nan  nan]\n",
      " [ nan  nan  nan  nan  nan  nan]\n",
      " [ nan  nan  nan  nan  nan  nan]\n",
      " [ nan  nan  nan  nan  nan  nan]]\n",
      "chi^2 =  0.00\n",
      "chi^2/d.f.=  inf\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/yury/Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/scipy/optimize/minpack.py:690: OptimizeWarning: Covariance of the parameters could not be estimated\n",
      "  category=OptimizeWarning)\n",
      "/Users/yury/Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/ipykernel/__main__.py:21: RuntimeWarning: invalid value encountered in double_scalars\n",
      "/Users/yury/Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/ipykernel/__main__.py:27: RuntimeWarning: divide by zero encountered in double_scalars\n"
     ]
    },
    {
     "data": {
      "image/png": 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IJIBms4iIJIDCXEQkARTmIiIJoDAXEUkAhbmISAIozEVEEkBhLiKSAApzEZEE\n+P8PWgkW+69U9gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x115899550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Nth-order poly function\n",
    "def modelN(*arg):\n",
    "    x = arg[0]\n",
    "    N = len(arg)-1\n",
    "    sum = arg[1]\n",
    "    for i in range(1,N):\n",
    "        sum += arg[i+1]*x**i\n",
    "    return sum\n",
    "\n",
    "N=5   # poly degree\n",
    "par0    = np.zeros(N+1)\n",
    "par[1]=1\n",
    "par, cov = fitter.curve_fit(modelN, xdata, ydata, par0, sigma)\n",
    "print par\n",
    "print cov\n",
    "\n",
    "corr = cov.copy() # copy shape\n",
    "# compute correlation matrix\n",
    "for i in range(len(par)):\n",
    "    for j in range(len(par)):\n",
    "        corr[i,j] = cov[i,j]/sqrt(cov[i,i]*cov[j,j])\n",
    "        \n",
    "print corr\n",
    "\n",
    "# compute reduced chi2\n",
    "chi_squared = np.sum(((modelN(xdata, *par)-ydata)/sigma)**2)\n",
    "reduced_chi_squared = (chi_squared)/(len(xdata)-len(par))\n",
    "print 'chi^2 = {0:5.2f}'.format(chi_squared)\n",
    "print 'chi^2/d.f.={0:5.2f}'.format(reduced_chi_squared)\n",
    "\n",
    "# overlay plot over data\n",
    "plt.errorbar(xdata, ydata, xerr=0, yerr=sigma, fmt='o')\n",
    "plt.xlim(-1,6)\n",
    "xfit = np.linspace(0,5,50)\n",
    "plt.plot(xfit,modelN(xfit,*par),'r-')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Caveat: correlations\n",
    "\n",
    "You may notice that poly parameters are highly correlated. You can reduce them by using *Chebychev polynomials*. Here is an example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 2.16666667  0.70285714]\n",
      "[[  6.28412704e-02   1.52261452e-10]\n",
      " [  1.52261452e-10   2.15455784e-02]]\n",
      "a= 2.167+/-0.251\n",
      "b= 0.703+/-0.147\n",
      "[[  1.00000000e+00   4.13798023e-09]\n",
      " [  4.13798023e-09   1.00000000e+00]]\n",
      "chi^2 =  1.51\n",
      "chi^2/d.f.= 0.38\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x115c71ad0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# linear function\n",
    "def modelC(x, a, b):\n",
    "    return a + b*(x-2.5)\n",
    "\n",
    "# Initial guess.\n",
    "par0    = np.array([0.0, 1.0])\n",
    "par, cov = fitter.curve_fit(modelC, xdata, ydata, par0, sigma)\n",
    "print par\n",
    "print cov\n",
    "\n",
    "# decode it now\n",
    "print 'a={0:6.3f}+/-{1:5.3f}'.format(par[0],sqrt(cov[0,0]))\n",
    "print 'b={0:6.3f}+/-{1:5.3f}'.format(par[1],sqrt(cov[1,1]))\n",
    "\n",
    "corr = cov.copy() # copy shape\n",
    "# compute correlation matrix\n",
    "for i in range(len(par)):\n",
    "    for j in range(len(par)):\n",
    "        corr[i,j] = cov[i,j]/sqrt(cov[i,i]*cov[j,j])\n",
    "        \n",
    "print corr\n",
    "\n",
    "# compute reduced chi2\n",
    "chi_squared = np.sum(((modelC(xdata, *par)-ydata)/sigma)**2)\n",
    "reduced_chi_squared = (chi_squared)/(len(xdata)-len(par))\n",
    "print 'chi^2 = {0:5.2f}'.format(chi_squared)\n",
    "print 'chi^2/d.f.={0:5.2f}'.format(reduced_chi_squared)\n",
    "\n",
    "# overlay plot over data\n",
    "plt.errorbar(xdata, ydata, xerr=0, yerr=sigma, fmt='o')\n",
    "plt.xlim(-1,6)\n",
    "xfit = np.linspace(0,5,50)\n",
    "plt.plot(xfit,modelC(xfit,par[0],par[1]),'r-')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Warning: Lack of robustness\n",
    "Gradient methods such as *Levenburg-Marquardt* used by *leastsq/curve_fit* are not robust and simply run into the nearest local minimum. Therefore, it is important to provide the initial set of values that are \"close enough\". Here is the demonstration below (courtesy https://python4mpia.github.io/fitting_data/least-squares-fitting.html)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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GudiYf20SHbOiDV84+iylzxO6LKVPUwbJ6CWjl5TehXHn0uDJGMjoow2kMwtiY5iJjqUF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AV2B/bDhFHa7hpymwo5b39Q35NTX7E5IiYiZNkrCypM2srKVhDRrX/+BE9Qn4f5U3SlmKj6gaxs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\nTExYUGGMMcaYmPj/4kqlBZ4YrAYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11819bd50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy,math\n",
    "import scipy.optimize as optimization\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Chose a model that will create bimodality.\n",
    "def func(x, a, b):\n",
    "    return a + b*b*x  # Term b*b will create bimodality.\n",
    "\n",
    "# Create toy data for curve_fit.\n",
    "xdata = numpy.array([0.0,1.0,2.0,3.0,4.0,5.0])\n",
    "ydata = numpy.array([0.1,0.9,2.2,2.8,3.9,5.1])\n",
    "sigma = numpy.array([1.0,1.0,1.0,1.0,1.0,1.0])\n",
    "\n",
    "# Compute chi-square manifold.\n",
    "Steps = 101  # grid size\n",
    "Chi2Manifold = numpy.zeros([Steps,Steps])  # allocate grid\n",
    "amin = -7.0  # minimal value of a covered by grid\n",
    "amax = +5.0  # maximal value of a covered by grid\n",
    "bmin = -4.0  # minimal value of b covered by grid\n",
    "bmax = +4.0  # maximal value of b covered by grid\n",
    "for s1 in range(Steps):\n",
    "    for s2 in range(Steps):\n",
    "        # Current values of (a,b) at grid position (s1,s2).\n",
    "        a = amin + (amax - amin)*float(s1)/(Steps-1)\n",
    "        b = bmin + (bmax - bmin)*float(s2)/(Steps-1)\n",
    "        # Evaluate chi-squared.\n",
    "        chi2 = 0.0\n",
    "        for n in range(len(xdata)):\n",
    "            residual = (ydata[n] - func(xdata[n], a, b))/sigma[n]\n",
    "            chi2 = chi2 + residual*residual\n",
    "        Chi2Manifold[Steps-1-s2,s1] = chi2  # write result to grid.\n",
    "\n",
    "# Plot grid.\n",
    "plt.figure(1, figsize=(8,4.5))\n",
    "plt.subplots_adjust(left=0.09, bottom=0.09, top=0.97, right=0.99)\n",
    "# Plot chi-square manifold.\n",
    "image = plt.imshow(Chi2Manifold, vmax=50.0,\n",
    "              extent=[amin, amax, bmin, bmax])\n",
    "# Plot where curve-fit is going to for a couple of initial guesses.\n",
    "for a_initial in -6.0, -4.0, -2.0, 0.0, 2.0, 4.0:\n",
    "    # Initial guess.\n",
    "    x0   = numpy.array([a_initial, -3.5])\n",
    "    xFit = optimization.curve_fit(func, xdata, ydata, x0, sigma)[0]\n",
    "    plt.plot([x0[0], xFit[0]], [x0[1], xFit[1]], 'o-', ms=4,\n",
    "                 markeredgewidth=0, lw=2, color='orange')\n",
    "plt.colorbar(image)  # make colorbar\n",
    "plt.xlim(amin, amax)\n",
    "plt.ylim(bmin, bmax)\n",
    "plt.xlabel(r'$a$', fontsize=24)\n",
    "plt.ylabel(r'$b$', fontsize=24)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example: histogram fitting \n",
    "\n",
    "Here is an example of an unbinned *max-likelihood* fit of a set of events to a Gaussian PDF\n",
    "Courtesy http://glowingpython.blogspot.com/2012/07/distribution-fitting-with-scipy.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(-0.036207592016358682, 1.1117025215657919)\n"
     ]
    },
    {
     "data": {
      "image/png": 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OxYQgS/Sm3IhZv4j07sOsbFOAju2z2bHhrNdhmBBkid6UC1FnTlBr93qOdBpI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\niMigMjimCaaMDHj5Zfjtb3M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z/x/b6YQqnDpUGgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1158dad90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import norm\n",
    "from numpy import linspace\n",
    "from pylab import plot,show,hist,figure,title\n",
    "\n",
    "# generate 100 events from a normal distrubution\n",
    "# with mean 0 and standard deviation 1\n",
    "sample = norm.rvs(loc=0,scale=1,size=100) \n",
    "\n",
    "par = norm.fit(sample) # distribution fitting\n",
    "\n",
    "#hist(sample,20)\n",
    "\n",
    "print par\n",
    "\n",
    "# now, par[0] and par[1] are the mean and \n",
    "# the standard deviation of the fitted distribution\n",
    "x = linspace(-5,5,100)\n",
    "# fitted distribution\n",
    "pdf_fitted = norm.pdf(x,loc=par[0],scale=par[1])\n",
    "# original distribution\n",
    "pdf = norm.pdf(x)\n",
    "\n",
    "title('Normal distribution')\n",
    "plot(x,pdf_fitted,'r-',x,pdf,'b-')\n",
    "hist(sample,normed=1,alpha=.3)\n",
    "show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}