dist_fitter_01.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1698,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import time\n",
    "import math\n",
    "\n",
    "from scipy import stats\n",
    "\n",
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\")\n",
    "\n",
    "\n",
    "ksN = 100           # Kolmogorov-Smirnov KS test for goodness of fit: samples\n",
    "ALPHA = 0.05        # significance level for hypothesis test"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1. Intro"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1699,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "from scipy.stats import (\n",
    "    norm, beta, expon, gamma, genextreme, logistic, lognorm, triang, uniform, fatiguelife,            \n",
    "    gengamma, gennorm, dweibull, dgamma, gumbel_r, powernorm, rayleigh, weibull_max, weibull_min, \n",
    "    laplace, alpha, genexpon, bradford, betaprime, burr, fisk, genpareto, hypsecant, \n",
    "    halfnorm, halflogistic, invgauss, invgamma, levy, loglaplace, loggamma, maxwell, \n",
    "    mielke, ncx2, ncf, nct, nakagami, pareto, lomax, powerlognorm, powerlaw, rice, \n",
    "    semicircular, trapezoid, rice, invweibull, foldnorm, foldcauchy, cosine, exponpow, \n",
    "    exponweib, wald, wrapcauchy, truncexpon, truncnorm, t, rdist\n",
    "    )\n",
    "\n",
    "\n",
    "distributions = [\n",
    "    norm, beta, expon, gamma, genextreme, logistic, lognorm, triang, uniform, fatiguelife,            \n",
    "    gengamma, gennorm, dweibull, dgamma, gumbel_r, powernorm, rayleigh, weibull_max, weibull_min, \n",
    "    laplace, alpha, genexpon, bradford, betaprime, burr, fisk, genpareto, hypsecant, \n",
    "    halfnorm, halflogistic, invgauss, invgamma, levy, loglaplace, loggamma, maxwell, \n",
    "    mielke, ncx2, ncf, nct, nakagami, pareto, lomax, powerlognorm, powerlaw, rice, \n",
    "    semicircular, trapezoid, rice, invweibull, foldnorm, foldcauchy, cosine, exponpow, \n",
    "    exponweib, wald, wrapcauchy, truncexpon, truncnorm, t, rdist\n",
    "    ]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1700,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "number of continuous distributions: 104\n",
      "number of discrete distributions:   19\n"
     ]
    }
   ],
   "source": [
    "dist_continu = [d for d in dir(stats) if\n",
    "                isinstance(getattr(stats, d), stats.rv_continuous)]\n",
    "dist_discrete = [d for d in dir(stats) if\n",
    "                 isinstance(getattr(stats, d), stats.rv_discrete)]\n",
    "print('number of continuous distributions: %d' % len(dist_continu))\n",
    "print('number of discrete distributions:   %d' % len(dist_discrete))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1701,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "No handles with labels found to put in legend.\n"
     ]
    },
    {
     "data": {
      "image/png": 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VXChYB3ydwY8/xy8UPGfBmEv50YuiH52WbPPGXst4L4r22W9nMLgIs31KP9ft86Z/jcGTyFORbcH4zzC+i6J99tup86Z/A9g7ZZ/r2cB13fRGBqcZnjIN2bpxzwbuoXvQcsr23U3ARd30zzE4h75kzrGFX+H/6LkM/hb/GvCO7r3LGRxVwuBvqb8DDgFfAJ4xRdl+kcERyX8x+KnhwBRl+yfgP4F93Wv3lH2ufwUc6LLdslypjjvbgrFjK/Se++3Puv12Z7ffnj1ln2sYnLI6COwHdkxLtm7+XcCfj3OfrWDfnQZ8vvts9wG/utz6fPRfkhoxjefQJUmrYKFLUiMsdElqhIUuSY2w0CWpERa6JDXCQpekRvwvnLpZNh0BJaYAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# example: properties of the beta distribution\n",
    "\n",
    "a, b = 2, 6\n",
    "\n",
    "x = beta.rvs(a, b, size=1000)\n",
    "\n",
    "fig, ax = plt.subplots(1, 1)\n",
    "ax.hist(x, density=True, histtype='stepfilled', alpha=0.2)\n",
    "ax.legend(loc='best', frameon=False)\n",
    "plt.show()\n",
    "pass"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1702,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'scipy.stats._continuous_distns.beta_gen'>\n"
     ]
    }
   ],
   "source": [
    "print(type(beta))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1703,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean : 0.250\n",
      "var : 0.021\n",
      "shape a : 0.000\n",
      "shape b : 1.000\n",
      "median : 0.228\n"
     ]
    }
   ],
   "source": [
    "# statistics of the Beta(2,6) distribution\n",
    "m = beta.mean(a,b)\n",
    "v = beta.var(a,b)\n",
    "shp_a = beta.a\n",
    "shp_b = beta.b\n",
    "median = beta.median(a,b)\n",
    "\n",
    "dict_stats = {\"mean\":m, \"var\":v, \"shape a\":shp_a, \"shape b\":shp_b, \"median\":median}\n",
    "_ = [print(k,\":\",f'{v:.3f}') for k,v in dict_stats.items()]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1704,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean : 0.250\n",
      "var : 0.021\n",
      "skew : 0.693\n",
      "kurt : 0.109\n"
     ]
    }
   ],
   "source": [
    "# first 4 moments of Beta(2,6)\n",
    "moments_values = beta.stats(a,b, moments=\"mvsk\")\n",
    "\n",
    "moments_names = [\"mean\", \"var\", \"skew\", \"kurt\"]\n",
    "moments = dict(zip(moments_names, moments_values))\n",
    "_ = [print(k,\":\",f'{v:.3f}') for k,v in moments.items()]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1705,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.250\n",
      "0.021\n",
      "0.693\n",
      "0.109\n"
     ]
    }
   ],
   "source": [
    "# freeze the distibution as an object with its current parameters, assign it to variable rv\n",
    "\n",
    "rv = beta(a,b)\n",
    "moments = rv.stats(\"mvsk\")\n",
    "_ = [print(f'{v:.3f}') for v in moments]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1706,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the pdf\n",
    "x = np.linspace(rv.ppf(0.01),\n",
    "                rv.ppf(0.99), 100)\n",
    "\n",
    "fig, ax = plt.subplots(1, 1)\n",
    "ax.plot(x, rv.pdf(x), 'r-', lw=5, alpha=0.6, label='beta pdf')\n",
    "pass"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1707,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0, 1.0)"
      ]
     },
     "execution_count": 1707,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rv.support()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1708,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.0, inf)"
      ]
     },
     "execution_count": 1708,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gamma(1,1).support()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1709,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(100.0, 320.0)\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# horizontally shift the beta distribution and rescale its right tail to \n",
    "\n",
    "loc, scl = 100, 220\n",
    "rv = beta(a,b, loc,scl)\n",
    "print(rv.support())\n",
    "\n",
    "x = np.linspace(rv.ppf(0.01),\n",
    "                rv.ppf(0.99), 100)\n",
    "\n",
    "fig, ax = plt.subplots(1, 1)\n",
    "ax.plot(x, rv.pdf(x), 'r-', lw=5, alpha=0.6, label='beta pdf')\n",
    "pass"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1710,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean : 155.000\n",
      "var : 1008.333\n",
      "skew : 0.693\n",
      "kurt : 0.109\n",
      "std : 31.754\n"
     ]
    }
   ],
   "source": [
    "# get the first 4 moments and append the std deviation\n",
    "\n",
    "moments_values = [v.item() for v in rv.stats(moments=\"mvsk\")]\n",
    "moments_values.append(rv.std())\n",
    "moments_names = [\"mean\", \"var\", \"skew\", \"kurt\", \"std\"]\n",
    "\n",
    "moments = dict(zip(moments_names, moments_values))\n",
    "_ = [print(k,\":\",f'{v:.3f}') for k,v in moments.items()]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1711,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the cdf\n",
    "\n",
    "fig, ax = plt.subplots(1, 1)\n",
    "ax.plot(x, rv.cdf(x), 'r-', lw=5, alpha=0.6, label='beta cdf')\n",
    "pass\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1712,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the inverse cdf or ppf\n",
    "\n",
    "q = np.linspace(0.0, 1.0, 100)\n",
    "\n",
    "fig, ax = plt.subplots(1, 1)\n",
    "ax.plot(q, rv.ppf(q), 'r-', lw=5, alpha=0.6, label='beta inverse cdf')\n",
    "pass\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1713,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100.0 : 0.0000 / 0.0000\n",
      "105.0 : 0.0100 / 0.0039\n",
      "120.0 : 0.1276 / 0.0108\n",
      "150.3 : 0.5000 / 0.0119\n",
      "155.0 : 0.5551 / 0.0113\n",
      "241.5 : 0.9900 / 0.0007\n",
      "300.0 : 1.0000 / 0.0000\n",
      "320.0 : 1.0000 / 0.0000\n"
     ]
    }
   ],
   "source": [
    "# cdf(x) and pdf(x) for selected points x\n",
    "xeval = [100.0, rv.ppf(0.01), 120.0, rv.median(), rv.mean(), rv.ppf(.99), 300.0, 320.0]\n",
    "cdfx = rv.cdf(xeval)\n",
    "pdfx = rv.pdf(xeval)\n",
    "_ = {print(f'{k:.1f}',\":\",f'{c:.4f}',\"/\",f'{p:.4f}') for k,c,p in zip(xeval, cdfx, pdfx)}\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1714,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100.000 : 100.000\n",
      "104.986 : 104.986\n",
      "120.000 : 120.000\n",
      "150.268 : 150.268\n",
      "155.000 : 155.000\n",
      "241.540 : 241.540\n",
      "300.000 : 300.000\n",
      "320.000 : 320.000\n"
     ]
    }
   ],
   "source": [
    "# percent point function / quantiles\n",
    "\n",
    "ppfq = rv.ppf(cdfx)\n",
    "\n",
    "_ = {print(f'{x:.3f}',\":\",f'{q:.3f}') for x,q in zip(xeval, ppfq)}\n",
    "assert(all(abs(xeval - ppfq)) < 1e-6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2. Fitting a Weibull Distribution to Model Time Till Failure"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1715,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "No handles with labels found to put in legend.\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# create synthetic observations for lifetime data by generating 1000 Weibull random variates\n",
    "# assume these are expert estimates\n",
    "\n",
    "shp, loc, scl = 1.5, 0, 50000\n",
    "\n",
    "rv = weibull_min(c=shp, loc=loc, scale=scl)\n",
    "\n",
    "data = rv.rvs(1000)\n",
    "\n",
    "fig, ax = plt.subplots(1, 1)\n",
    "ax.hist(data, density=True, histtype='stepfilled', alpha=0.2)\n",
    "ax.legend(loc='best', frameon=False)\n",
    "plt.show()\n",
    "pass"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1716,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.1056335329791707"
      ]
     },
     "execution_count": 1716,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.skew(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1717,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "shape : 1.525\n",
      "loc : 0.000\n",
      "shape : 49839.178\n"
     ]
    }
   ],
   "source": [
    "# distribution fitter and KS test\n",
    "\n",
    "# we decide to fix one of the parameters, the location, at its known value of 0, by entering the keyword 'floc'\n",
    "# if left flexible, a location paramater can exert a massive influence on shape and scale\n",
    "    \n",
    "params = weibull_min.fit(data, floc=0)\n",
    "\n",
    "param_names = [\"shape\", \"loc\", \"shape\"]\n",
    "dict_param = {print(k,\":\",f'{v:.3f}') for k,v in zip(param_names, params)}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1718,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.883\n"
     ]
    }
   ],
   "source": [
    "# KS test for goodness of fit: p-value > 0.05 =\n",
    "ks = stats.kstest(data, weibull_min.name, params, ksN)[1]   # return p-value\n",
    "print(f'{ks:.3f}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1719,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the actual data and the fitted weibull pdf\n",
    "rv = weibull_min(shp, loc, scl)\n",
    "\n",
    "x = np.linspace(rv.ppf(0.01),\n",
    "                rv.ppf(0.99), 100)\n",
    "\n",
    "fig, ax = plt.subplots(1, 1)\n",
    "ax.hist(data, density=True, histtype='stepfilled', alpha=0.2)\n",
    "ax.plot(x, rv.pdf(x), 'r-', lw=5, alpha=0.6, label='beta pdf')\n",
    "pass"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1720,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "45137\n"
     ]
    }
   ],
   "source": [
    "# mean time to failure\n",
    "print(f'{rv.mean():.0f}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1721,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "at hours : 20000.000\n",
      "% cumulative failures : 0.224\n",
      "surviving % of all components : 0.776\n"
     ]
    }
   ],
   "source": [
    "T = 20000\n",
    "\n",
    "cdfT = rv.cdf(T)           # cumulative failure rate after T hours\n",
    "\n",
    "svfT = 1 - cdfT\n",
    "svfT = rv.sf(T)\n",
    "\n",
    "dict_f = {\"at hours\":T, \"% cumulative failures\":cdfT, \"surviving % of all components\":svfT}\n",
    "_ = [print(k,\":\",f'{v:.3f}') for k,v in dict_f.items()]\n",
    "# svf % of all components will last at least T hours"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1722,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "at hours : 10000.000\n",
      "% cumulative failures : 0.086\n",
      "surviving % of all components : 0.914\n"
     ]
    }
   ],
   "source": [
    "T = 10000\n",
    "\n",
    "cdfT = rv.cdf(T)           # cumulative failure rate after T hours\n",
    "\n",
    "svfT = 1 - cdfT\n",
    "svfT = rv.sf(T)\n",
    "\n",
    "dict_f = {\"at hours\":T, \"% cumulative failures\":cdfT, \"surviving % of all components\":svfT}\n",
    "_ = [print(k,\":\",f'{v:.3f}') for k,v in dict_f.items()]\n",
    "# svf % of all components will last at least T hours"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1723,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "at hours : 500.000\n",
      "% cumulative failures : 0.001\n",
      "surviving % of all components : 0.999\n"
     ]
    }
   ],
   "source": [
    "T = 500\n",
    "\n",
    "cdfT = rv.cdf(T)           # cumulative failure rate after T hours\n",
    "\n",
    "svfT = 1 - cdfT\n",
    "svfT = rv.sf(T)\n",
    "\n",
    "dict_f = {\"at hours\":T, \"% cumulative failures\":cdfT, \"surviving % of all components\":svfT}\n",
    "_ = [print(k,\":\",f'{v:.3f}') for k,v in dict_f.items()]\n",
    "# svf % of all components will last at least T hours"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1724,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2329 hours\n"
     ]
    }
   ],
   "source": [
    "# time to a cumulative failure rate of 1%\n",
    "\n",
    "q = 0.01\n",
    "ppfq = rv.ppf(q)           \n",
    "\n",
    "print(f'{ppfq:.0f}', \"hours\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3. The Auto-Fitter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1725,
   "metadata": {},
   "outputs": [],
   "source": [
    "# KS test for goodness of fit\n",
    "\n",
    "def kstest(data, distname, paramtup):\n",
    "    ks = stats.kstest(data, distname, paramtup, ksN)[1]   # return p-value\n",
    "    return ks             # return p-value\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1726,
   "metadata": {},
   "outputs": [],
   "source": [
    "# distribution fitter and call to KS test\n",
    "\n",
    "def fitdist(data, dist):    \n",
    "    fitted = dist.fit(data, floc=0.0)\n",
    "    ks = kstest(data, dist.name, fitted)\n",
    "    res = (dist.name, ks, *fitted)\n",
    "    return res"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1727,
   "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>distribution</th>\n",
       "      <th>KS p-value</th>\n",
       "      <th>param1</th>\n",
       "      <th>param2</th>\n",
       "      <th>param3</th>\n",
       "      <th>param4</th>\n",
       "      <th>param5</th>\n",
       "      <th>distobj</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>weibull_min</td>\n",
       "      <td>0.883</td>\n",
       "      <td>1.525</td>\n",
       "      <td>0.000</td>\n",
       "      <td>49,839.178</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>&lt;scipy.stats._continuous_distns.weibull_min_ge...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>beta</td>\n",
       "      <td>0.552</td>\n",
       "      <td>1.742</td>\n",
       "      <td>10.475</td>\n",
       "      <td>0.000</td>\n",
       "      <td>314,806.815</td>\n",
       "      <td>NaN</td>\n",
       "      <td>&lt;scipy.stats._continuous_distns.beta_gen objec...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>burr</td>\n",
       "      <td>0.528</td>\n",
       "      <td>4.025</td>\n",
       "      <td>0.325</td>\n",
       "      <td>0.000</td>\n",
       "      <td>65,946.527</td>\n",
       "      <td>NaN</td>\n",
       "      <td>&lt;scipy.stats._continuous_distns.burr_gen objec...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>mielke</td>\n",
       "      <td>0.528</td>\n",
       "      <td>1.310</td>\n",
       "      <td>4.025</td>\n",
       "      <td>0.000</td>\n",
       "      <td>65,946.689</td>\n",
       "      <td>NaN</td>\n",
       "      <td>&lt;scipy.stats._continuous_distns.mielke_gen obj...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>ncf</td>\n",
       "      <td>0.441</td>\n",
       "      <td>0.003</td>\n",
       "      <td>37.906</td>\n",
       "      <td>10.706</td>\n",
       "      <td>0.000</td>\n",
       "      <td>10.030</td>\n",
       "      <td>&lt;scipy.stats._continuous_distns.ncf_gen object...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>56</th>\n",
       "      <td>trapezoid</td>\n",
       "      <td>0.000</td>\n",
       "      <td>1.000</td>\n",
       "      <td>1.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>208,482.388</td>\n",
       "      <td>NaN</td>\n",
       "      <td>&lt;scipy.stats._continuous_distns.trapezoid_gen ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>57</th>\n",
       "      <td>exponpow</td>\n",
       "      <td>0.000</td>\n",
       "      <td>1.985</td>\n",
       "      <td>0.000</td>\n",
       "      <td>31.645</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>&lt;scipy.stats._continuous_distns.exponpow_gen o...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>58</th>\n",
       "      <td>alpha</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>2,185.492</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>&lt;scipy.stats._continuous_distns.alpha_gen obje...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>59</th>\n",
       "      <td>weibull_max</td>\n",
       "      <td>0.000</td>\n",
       "      <td>1.500</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>&lt;scipy.stats._continuous_distns.weibull_max_ge...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>60</th>\n",
       "      <td>truncnorm</td>\n",
       "      <td>0.000</td>\n",
       "      <td>1.185</td>\n",
       "      <td>1.327</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>&lt;scipy.stats._continuous_distns.truncnorm_gen ...</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>61 rows × 8 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   distribution  KS p-value  param1  param2     param3      param4  param5  \\\n",
       "0   weibull_min       0.883   1.525   0.000 49,839.178         NaN     NaN   \n",
       "1          beta       0.552   1.742  10.475      0.000 314,806.815     NaN   \n",
       "2          burr       0.528   4.025   0.325      0.000  65,946.527     NaN   \n",
       "3        mielke       0.528   1.310   4.025      0.000  65,946.689     NaN   \n",
       "4           ncf       0.441   0.003  37.906     10.706       0.000  10.030   \n",
       "..          ...         ...     ...     ...        ...         ...     ...   \n",
       "56    trapezoid       0.000   1.000   1.000      0.000 208,482.388     NaN   \n",
       "57     exponpow       0.000   1.985   0.000     31.645         NaN     NaN   \n",
       "58        alpha       0.000   0.000   0.000  2,185.492         NaN     NaN   \n",
       "59  weibull_max       0.000   1.500   0.000      0.000         NaN     NaN   \n",
       "60    truncnorm       0.000   1.185   1.327      0.000       0.000     NaN   \n",
       "\n",
       "                                              distobj  \n",
       "0   <scipy.stats._continuous_distns.weibull_min_ge...  \n",
       "1   <scipy.stats._continuous_distns.beta_gen objec...  \n",
       "2   <scipy.stats._continuous_distns.burr_gen objec...  \n",
       "3   <scipy.stats._continuous_distns.mielke_gen obj...  \n",
       "4   <scipy.stats._continuous_distns.ncf_gen object...  \n",
       "..                                                ...  \n",
       "56  <scipy.stats._continuous_distns.trapezoid_gen ...  \n",
       "57  <scipy.stats._continuous_distns.exponpow_gen o...  \n",
       "58  <scipy.stats._continuous_distns.alpha_gen obje...  \n",
       "59  <scipy.stats._continuous_distns.weibull_max_ge...  \n",
       "60  <scipy.stats._continuous_distns.truncnorm_gen ...  \n",
       "\n",
       "[61 rows x 8 columns]"
      ]
     },
     "execution_count": 1727,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# call fitting function for all distributions in list\n",
    "res = [fitdist(data,D) for D in distributions]\n",
    "\n",
    "# convert the fitted list of tuples to dataframe\n",
    "pd.options.display.float_format = '{:,.3f}'.format\n",
    "df = pd.DataFrame(res, columns=[\"distribution\", \"KS p-value\", \"param1\", \"param2\", \"param3\", \"param4\", \"param5\"])\n",
    "df[\"distobj\"] = distributions\n",
    "df.sort_values(by=[\"KS p-value\"], inplace=True, ascending=False)\n",
    "df.reset_index(inplace=True)\n",
    "df.drop(\"index\", axis=1, inplace=True)\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1728,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "def plot_fitted_pdf(df):\n",
    "    \n",
    "    N = len(df)\n",
    "    chrows = math.ceil(N/3)                    # how many rows of charts if 3 in a row\n",
    "    fig, ax = plt.subplots(chrows, 3, figsize=(20, 5 * chrows))\n",
    "    ax = ax.ravel()\n",
    "    dfRV = pd.DataFrame()\n",
    "\n",
    "    for i in df.index:\n",
    "\n",
    "        # D_row = df.iloc[i,:-1]\n",
    "        D_name = df.iloc[i,0]\n",
    "        D = df.iloc[i,7]\n",
    "        KSp = df.iloc[i,1]\n",
    "        params = df.iloc[i,2:7]    \n",
    "        params = [p for p in params if ~np.isnan(p)]\n",
    "\n",
    "        # calibrate x-axis by finding the 1% and 99% quantiles in percent point function\n",
    "        x = np.linspace(\n",
    "                    D.ppf(0.01, *params), \n",
    "                    D.ppf(0.99, *params), 100)\n",
    "\n",
    "        #fig, ax = plt.subplots(1, 1)\n",
    "        # plot histogram of actual observations\n",
    "        ax[i].hist(data, density=True, histtype='stepfilled', alpha=0.2)\n",
    "        # plot fitted distribution\n",
    "        rv = D(*params)\n",
    "        title = f'pdf {D_name}, with p(KS): {KSp:.2f}' \n",
    "        ax[i].plot(x, rv.pdf(x), 'r-', lw=2, label=title)\n",
    "        ax[i].legend(loc=\"upper right\", frameon=False)    \n",
    "\n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1729,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(8, 8)\n",
      "Fitted Distributions with KS p-values > ALPHA:\n"
     ]
    },
    {
     "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>distribution</th>\n",
       "      <th>KS p-value</th>\n",
       "      <th>param1</th>\n",
       "      <th>param2</th>\n",
       "      <th>param3</th>\n",
       "      <th>param4</th>\n",
       "      <th>param5</th>\n",
       "      <th>distobj</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>weibull_min</td>\n",
       "      <td>0.883</td>\n",
       "      <td>1.525</td>\n",
       "      <td>0.000</td>\n",
       "      <td>49,839.178</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>&lt;scipy.stats._continuous_distns.weibull_min_ge...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>beta</td>\n",
       "      <td>0.552</td>\n",
       "      <td>1.742</td>\n",
       "      <td>10.475</td>\n",
       "      <td>0.000</td>\n",
       "      <td>314,806.815</td>\n",
       "      <td>NaN</td>\n",
       "      <td>&lt;scipy.stats._continuous_distns.beta_gen objec...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>burr</td>\n",
       "      <td>0.528</td>\n",
       "      <td>4.025</td>\n",
       "      <td>0.325</td>\n",
       "      <td>0.000</td>\n",
       "      <td>65,946.527</td>\n",
       "      <td>NaN</td>\n",
       "      <td>&lt;scipy.stats._continuous_distns.burr_gen objec...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>mielke</td>\n",
       "      <td>0.528</td>\n",
       "      <td>1.310</td>\n",
       "      <td>4.025</td>\n",
       "      <td>0.000</td>\n",
       "      <td>65,946.689</td>\n",
       "      <td>NaN</td>\n",
       "      <td>&lt;scipy.stats._continuous_distns.mielke_gen obj...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>ncf</td>\n",
       "      <td>0.441</td>\n",
       "      <td>0.003</td>\n",
       "      <td>37.906</td>\n",
       "      <td>10.706</td>\n",
       "      <td>0.000</td>\n",
       "      <td>10.030</td>\n",
       "      <td>&lt;scipy.stats._continuous_distns.ncf_gen object...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>nakagami</td>\n",
       "      <td>0.326</td>\n",
       "      <td>0.665</td>\n",
       "      <td>0.000</td>\n",
       "      <td>54,057.857</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>&lt;scipy.stats._continuous_distns.nakagami_gen o...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>exponweib</td>\n",
       "      <td>0.318</td>\n",
       "      <td>1.832</td>\n",
       "      <td>1.107</td>\n",
       "      <td>0.000</td>\n",
       "      <td>33,181.632</td>\n",
       "      <td>NaN</td>\n",
       "      <td>&lt;scipy.stats._continuous_distns.exponweib_gen ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>gamma</td>\n",
       "      <td>0.154</td>\n",
       "      <td>1.986</td>\n",
       "      <td>0.000</td>\n",
       "      <td>22,612.325</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>&lt;scipy.stats._continuous_distns.gamma_gen obje...</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  distribution  KS p-value  param1  param2     param3      param4  param5  \\\n",
       "0  weibull_min       0.883   1.525   0.000 49,839.178         NaN     NaN   \n",
       "1         beta       0.552   1.742  10.475      0.000 314,806.815     NaN   \n",
       "2         burr       0.528   4.025   0.325      0.000  65,946.527     NaN   \n",
       "3       mielke       0.528   1.310   4.025      0.000  65,946.689     NaN   \n",
       "4          ncf       0.441   0.003  37.906     10.706       0.000  10.030   \n",
       "5     nakagami       0.326   0.665   0.000 54,057.857         NaN     NaN   \n",
       "6    exponweib       0.318   1.832   1.107      0.000  33,181.632     NaN   \n",
       "7        gamma       0.154   1.986   0.000 22,612.325         NaN     NaN   \n",
       "\n",
       "                                             distobj  \n",
       "0  <scipy.stats._continuous_distns.weibull_min_ge...  \n",
       "1  <scipy.stats._continuous_distns.beta_gen objec...  \n",
       "2  <scipy.stats._continuous_distns.burr_gen objec...  \n",
       "3  <scipy.stats._continuous_distns.mielke_gen obj...  \n",
       "4  <scipy.stats._continuous_distns.ncf_gen object...  \n",
       "5  <scipy.stats._continuous_distns.nakagami_gen o...  \n",
       "6  <scipy.stats._continuous_distns.exponweib_gen ...  \n",
       "7  <scipy.stats._continuous_distns.gamma_gen obje...  "
      ]
     },
     "execution_count": 1729,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# from dataframe, select distributions with high KS p-value\n",
    "df_ks = df.loc[df[\"KS p-value\"] > ALPHA]\n",
    "print(df_ks.shape)\n",
    "print(\"Fitted Distributions with KS p-values > ALPHA:\")\n",
    "df_ks\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1730,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1440x1080 with 9 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# call the plotting function\n",
    "plot_fitted_pdf(df_ks)\n",
    "pass"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1731,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "distribution                                          weibull_min\n",
       "KS p-value                                                  0.883\n",
       "param1                                                      1.525\n",
       "param2                                                      0.000\n",
       "param3                                                 49,839.178\n",
       "param4                                                        NaN\n",
       "param5                                                        NaN\n",
       "distobj         <scipy.stats._continuous_distns.weibull_min_ge...\n",
       "Name: 0, dtype: object"
      ]
     },
     "execution_count": 1731,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# fitted distribution with highest p-value of KS test\n",
    "D_opt = df_ks.loc[df_ks[\"KS p-value\"].idxmax()]\n",
    "# D_opt[:-1]\n",
    "D_opt\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1732,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "weibull_min\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[1.525384222021152, 0.0, 49839.17767175549]"
      ]
     },
     "execution_count": 1732,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# script takes this best fitting distribution and begins to works with it:\n",
    "# parameters\n",
    "\n",
    "print(D_opt.iloc[0])            # name\n",
    "DO = D_opt.iloc[7]              # distribution object\n",
    "\n",
    "params = D_opt.iloc[2:7]    \n",
    "params = [p for p in params if ~np.isnan(p)]\n",
    "params\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1733,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean : 44903.7020\n",
      "variance : 901247858.3014\n",
      "skew : 1.0427\n",
      "kurtosis : 1.2940\n"
     ]
    }
   ],
   "source": [
    "# statistics of the best fitting distribution\n",
    "stats = DO.stats(*params, \"mvsk\")\n",
    "stat_names = [\"mean\", \"variance\", \"skew\", \"kurtosis\"]\n",
    "dict_stats = {k:v for k,v in zip(stat_names, stats)} \n",
    "_ = [print(k,\":\",f'{v:.4f}') for k,v in dict_stats.items()]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1734,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5738388332003941"
      ]
     },
     "execution_count": 1734,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# CDF of a chosen x, here the mean\n",
    "x = dict_stats[\"mean\"]\n",
    "cdfx = DO.cdf(x, *params)\n",
    "cdfx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1735,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "44903.70200843498"
      ]
     },
     "execution_count": 1735,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# cross-check: if we insert the CDF's probability in the percent point function ppf,\n",
    "# will we get the mean as the quantile?\n",
    "ppfq = DO.ppf(cdfx, *params)\n",
    "assert abs(ppfq - x) < 1e-9\n",
    "ppfq"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1736,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "39194.07435010098"
      ]
     },
     "execution_count": 1736,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# cross-check: if we insert the CDF's probability in the percent point function ppf,\n",
    "# will we get the mean as the quantile?\n",
    "ppfq = DO.ppf(0.5, *params)\n",
    "ppfq"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1737,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0, inf)"
      ]
     },
     "execution_count": 1737,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# support [min, max] of distribution:\n",
    "DO.support(*params)"
   ]
  }
 ],
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  "interpreter": {
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  "kernelspec": {
   "display_name": "Python 3.8.5 64-bit ('ho03': conda)",
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  "language_info": {
   "codemirror_mode": {
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   "file_extension": ".py",
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