Inverse Transform Sampling .ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Sampling From a Probability Distribution\n",
    "\n",
    "# Inverse Transform Sampling."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "rayleigh_sample = np.random.rayleigh(scale = 13.5, size=50)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0,0.5,'Frequency (X=k)')"
      ]
     },
     "execution_count": 5,
     "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": [
    "plt.hist(rayleigh_sample)\n",
    "\n",
    "plt.xlabel(\"k\")\n",
    "\n",
    "plt.ylabel(\"Frequency (X=k)\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "rayleigh_sample = np.random.normal(loc =0, scale=1 ,size=300000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0,0.5,'Frequency (X=k)')"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZsAAAEKCAYAAADEovgeAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMi4zLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvIxREBQAAFhZJREFUeJzt3X+wZGV95/H3x0ECmCAYxl8MOrjOmhATCxyRLJtNVhQHUHBrYxZ1wxQhmZTBVXe1klE3C+WPFFZcUUolITIrGJTgjxUMuJMRf2S3SoFBUUB0mUIWRohMMgiICqLf/aOfK53h3jvNzH3umel5v6pudZ/vebrPt7uo+XDOefqcVBWSJPX0mKEbkCRNP8NGktSdYSNJ6s6wkSR1Z9hIkrozbCRJ3Rk2kqTuDBtJUneGjSSpu72GbmBXcdBBB9Xy5cuHbkOSdivXXnvtP1bV0u2NM2ya5cuXs3HjxqHbkKTdSpL/N8k4D6NJkrozbCRJ3Rk2kqTuDBtJUneGjSSpO8NGktSdYSNJ6s6wkSR1Z9hIkrrzCgLShJavvXyQ7d561gmDbFdaSO7ZSJK6M2wkSd0ZNpKk7gwbSVJ3ho0kqbtuYZNkXZK7ktwwVntCkg1Jbm6PB7Z6kpyTZFOSryc5Yuw1q9v4m5OsHqs/N8n17TXnJMl825AkDafnns2HgFXb1NYCV1bVCuDKtgxwHLCi/a0BzoVRcABnAM8HjgTOGAuPc9vYmdet2s42JEkD6RY2VfX3wNZtyicBF7TnFwAvG6tfWCNfBg5I8hTgxcCGqtpaVXcDG4BVbd3+VfWlqirgwm3ea7ZtSJIGstjnbJ5UVXcCtMcntvrBwO1j4za32nz1zbPU59vGIyRZk2Rjko1btmzZ4Q8lSZrfrjJBILPUagfqj0pVnVdVK6tq5dKlSx/tyyVJE1rssPluOwRGe7yr1TcDh4yNWwbcsZ36slnq821DkjSQxQ6by4CZGWWrgUvH6qe0WWlHAfe0Q2DrgWOTHNgmBhwLrG/r7ktyVJuFdso27zXbNiRJA+l2Ic4kHwV+CzgoyWZGs8rOAi5JchpwG/DyNvwK4HhgE/AD4FSAqtqa5G3ANW3cW6tqZtLBqxnNeNsX+Ez7Y55tSJIG0i1squoVc6w6ZpaxBZw+x/usA9bNUt8IPHuW+j/Ntg1J0nB2lQkCkqQpZthIkrozbCRJ3Rk2kqTuDBtJUneGjSSpO8NGktSdYSNJ6s6wkSR1Z9hIkrozbCRJ3Rk2kqTuDBtJUneGjSSpO8NGktSdYSNJ6s6wkSR1Z9hIkrozbCRJ3Rk2kqTuDBtJUneGjSSpO8NGktSdYSNJ6s6wkSR1Z9hIkrozbCRJ3Rk2kqTuDBtJUneGjSSpu0HCJsl/TnJjkhuSfDTJPkkOTXJVkpuT/E2SvdvYn2vLm9r65WPv86ZW/1aSF4/VV7XapiRrF/8TSpLGLXrYJDkYeC2wsqqeDSwBTgbeCZxdVSuAu4HT2ktOA+6uqmcCZ7dxJDmsve5XgFXAB5IsSbIEeD9wHHAY8Io2VpI0kL0G3O6+SX4M7AfcCbwAeGVbfwFwJnAucFJ7DvBx4H1J0uoXV9UDwLeTbAKObOM2VdUtAEkubmO/0fkzSV0sX3v5YNu+9awTBtu2psui79lU1XeAdwG3MQqZe4Brge9V1UNt2Gbg4Pb8YOD29tqH2vhfHK9v85q56pKkgQxxGO1ARnsahwJPBR7H6JDXtmrmJXOse7T12XpZk2Rjko1btmzZXuuSpB00xASBFwLfrqotVfVj4JPAvwIOSDJzWG8ZcEd7vhk4BKCtfzywdby+zWvmqj9CVZ1XVSurauXSpUsX4rNJkmYxRNjcBhyVZL927uUYRudTPg/8dhuzGri0Pb+sLdPWf66qqtVPbrPVDgVWAFcD1wAr2uy2vRlNIrhsET6XJGkOiz5BoKquSvJx4CvAQ8BXgfOAy4GLk7y91c5vLzkf+HCbALCVUXhQVTcmuYRRUD0EnF5VPwFI8hpgPaOZbuuq6sbF+nySpEcaZDZaVZ0BnLFN+RYenk02PvZHwMvneJ93AO+YpX4FcMXOdypJWgheQUCS1J1hI0nqzrCRJHVn2EiSupt3gkCSfYCXAL/B6AeYPwRuAC53hpckaVJzhk2SM4GXAl8ArgLuAvYB/iVwVguiN1TV1/u3KUnanc23Z3NNVZ05x7p3J3ki8LSFb0mSNG3mPGdTVZcDjN8/ZkaS51XVXVW1sV9rkqRpMckEgU+2e9AAkOQ3gXX9WpIkTZtJwuYPgU8leXKS44H3Asf3bUuSNE22e7maqromyWuBvwN+BLyoqrwevyRpYvPNRvs0//w+MPsxunHZ+UmoqhN7NydJmg7z7dm8a9G6kCRNtTnDpqq+uJiNSJKm10SXq2n3jfnZoyRJj8ak10Z7Zntc0asRSdL08kKckqTuDBtJUneGjSSpu0nDJl27kCRNtUnD5s+3eZQkaWIThU1VfWT8Mcl2L3MjSdKMOcMmyaeTPH2W+guB67p2JUmaKvPt2VwMfD7JW5I8NslT24863w6sXpz2JEnTYL6bp10EHM7obpw3AV8CPgv8elVduzjtSZKmwfbO2RwGHAlcDTwAPIkJbksgSdK4+c7ZfBB4P/BHVfVKRns5jwe+luTYRepPkjQF5tuzuRF4XlV9CaCq7q+qNwL/AfjTxWhOkjQd5rvFwNlz1K8HfqNbR5KkqTPfYbTzkvzqHOsel+T3kryqX2uSpGkx38n+DwB/2gLnBmALsA+j2wzsD6wDLureoTRm+drLh25B0g6Yb+rzdVX1O8DzGE0U+N/AZcDvV9Vzquq9VfXAjmw0yQFJPp7km0luSvLrSZ6QZEOSm9vjgW1skpyTZFOSryc5Yux9VrfxNydZPVZ/bpLr22vOSeK13SRpQNu9XE1Vfb+qvlBVH62qT1XVtxZgu+8F/ldV/RLwHEa/41kLXFlVK4Ar2zLAcYz2plYAa4BzAZI8ATgDeD6j6dlnzARUG7Nm7HWrFqBnSdIOWvRbDCTZH/g3wPkAVfVgVX0POAm4oA27AHhZe34ScGGNfBk4IMlTgBcDG6pqa1XdDWwAVrV1+1fVl6qqgAvH3kuSNIAh7mfzDEbnf/5Hkq8m+WCSxwFPqqo7AdrjE9v4g4Hbx16/udXmq2+epf4ISdYk2Zhk45YtW3b+k0mSZrXdsEny7AXe5l7AEcC5VXU4cD8PHzKbtYVZarUD9UcWq86rqpVVtXLp0qXzdy1J2mGT7Nn8RZKrk/xRkgMWYJubgc1VdVVb/jij8PluOwRGe7xrbPwhY69fBtyxnfqyWeqSpIFMMkHgXwOvYvQP+8YkH0nyoh3dYFX9A3B7kme10jHANxjNdJuZUbYauLQ9vww4pc1KOwq4px1mWw8cm+TANjHgWGB9W3dfkqPaLLRTxt5LkjSAiS6qWVU3J/mvwEbgHODw9g/5m6vqkzuw3f8EXJRkb+AW4FRGwXdJktOA24CXt7FXAMcDm4AftLFU1dYkbwOuaePeWlVb2/NXAx8C9gU+0/4kSQPZbtgk+TVG/8CfwGjG10ur6itJnsrotgOPOmyq6jpg5SyrjpllbAGnz/E+6xj9uHTb+kZgoc81SZJ20CR7Nu8D/orRXswPZ4pVdUfb25EkaV6ThM3xwA+r6icASR4D7FNVP6iqD3ftTpI0FSaZjfZZRuc+ZuzXapIkTWSSsNmnqr4/s9Ce79evJUnStJkkbO7f5uKXzwV+OM94SZL+mUnO2bwe+FiSmR9GPoXR3TolSZrIdsOmqq5J8kvAsxhdCuabVfXj7p1JkqbGRD/qZHRPm+Vt/OFJqKoLu3UlSZoqk/yo88PAvwCuA37SyjOX7pckabsm2bNZCRzWfskvSdKjNslstBuAJ/duRJI0vSbZszkI+EaSq4EHZopVdWK3riRJU2WSsDmzdxOSpOk2ydTnLyZ5OrCiqj6bZD9gSf/WJEnTYpLbQv8Bo7tp/mUrHQx8qmdTkqTpMskEgdOBo4F7YXQjNeCJPZuSJE2XScLmgap6cGYhyV6MfmcjSdJEJgmbLyZ5M7BvkhcBHwM+3bctSdI0mSRs1gJbgOuBPwSuALxDpyRpYpPMRvspo9tC/1X/diRJ02iSa6N9m1nO0VTVM7p0JEmaOpNeG23GPsDLgSf0aUeSNI22e86mqv5p7O87VfUe4AWL0JskaUpMchjtiLHFxzDa0/mFbh1JkqbOJIfR/vvY84eAW4Hf6dKNJGkqTTIb7d8uRiOSpOk1yWG0/zLf+qp698K1I0maRpPORnsecFlbfinw98DtvZqSJE2XSW+edkRV3QeQ5EzgY1X1+z0bkyRNj0kuV/M04MGx5QeB5V26kSRNpUnC5sPA1UnOTHIGcBVw4c5uOMmSJF9N8rdt+dAkVyW5OcnfJNm71X+uLW9q65ePvcebWv1bSV48Vl/VapuSrN3ZXiVJO2eSH3W+AzgVuBv4HnBqVf3ZAmz7dcBNY8vvBM6uqhVtW6e1+mnA3VX1TODsNo4khwEnA78CrAI+0AJsCfB+4DjgMOAVbawkaSCT7NkA7AfcW1XvBTYnOXRnNppkGXAC8MG2HEZXJfh4G3IB8LL2/KS2TFt/TBt/EnBxVT1QVd8GNgFHtr9NVXVLuw/PxW2sJGkgk9wW+gzgT4A3tdJjgb/eye2+B/hj4Kdt+ReB71XVQ215M6PbT9Mebwdo6+9p439W3+Y1c9UlSQOZZM/m3wEnAvcDVNUd7MTlapK8BLirqq4dL88ytLaz7tHWZ+tlTZKNSTZu2bJlnq4lSTtjkrB5sKqK9g92ksft5DaPBk5MciujQ1wvYLSnc0C75TTAMuCO9nwzcEjb9l7A44Gt4/VtXjNX/RGq6ryqWllVK5cuXbqTH0uSNJdJwuaSJH/JKAz+APgsO3Ejtap6U1Utq6rljE7wf66qXgV8HvjtNmw1cGl7fllbpq3/XAu/y4CT22y1Q4EVwNXANcCKNrtt77aNmR+kSpIGMMm10d6V5EXAvcCzgP9WVRs69PInwMVJ3g58FTi/1c8HPpxkE6M9mpNbXzcmuQT4BqMLhJ5eVT8BSPIaYD2wBFhXVTd26FeSNKF5w6ZNI15fVS8EFjxgquoLwBfa81sYzSTbdsyPGN2wbbbXvwN4xyz1K4ArFrBVSdJOmPcwWttT+EGSxy9SP5KkKTTJtdF+BFyfZANtRhpAVb22W1eSpKkySdhc3v4kSdohc4ZNkqdV1W1VdcFcYyRJmsR852w+NfMkyScWoRdJ0pSaL2zGf4n/jN6NSJKm13xhU3M8lyTpUZlvgsBzktzLaA9n3/actlxVtX/37iRJU2HOsKmqJYvZiCRpek16PxtJknaYYSNJ6s6wkSR1Z9hIkrozbCRJ3Rk2kqTuDBtJUneGjSSpO8NGktTdJPezkbSHWr52mFtZ3XrWCYNsV/24ZyNJ6s6wkSR1Z9hIkrozbCRJ3Rk2kqTuDBtJUneGjSSpO8NGktSdYSNJ6s6wkSR1Z9hIkrozbCRJ3S162CQ5JMnnk9yU5MYkr2v1JyTZkOTm9nhgqyfJOUk2Jfl6kiPG3mt1G39zktVj9ecmub695pwkWezPKUl62BB7Ng8Bb6iqXwaOAk5PchiwFriyqlYAV7ZlgOOAFe1vDXAujMIJOAN4PnAkcMZMQLUxa8Zet2oRPpckaQ6LHjZVdWdVfaU9vw+4CTgYOAm4oA27AHhZe34ScGGNfBk4IMlTgBcDG6pqa1XdDWwAVrV1+1fVl6qqgAvH3kuSNIBBz9kkWQ4cDlwFPKmq7oRRIAFPbMMOBm4fe9nmVpuvvnmW+mzbX5NkY5KNW7Zs2dmPI0maw2Bhk+TngU8Ar6+qe+cbOkutdqD+yGLVeVW1sqpWLl26dHstS5J20CBhk+SxjILmoqr6ZCt/tx0Coz3e1eqbgUPGXr4MuGM79WWz1CVJAxliNlqA84GbqurdY6suA2ZmlK0GLh2rn9JmpR0F3NMOs60Hjk1yYJsYcCywvq27L8lRbVunjL2XJGkAew2wzaOB3wWuT3Jdq70ZOAu4JMlpwG3Ay9u6K4DjgU3AD4BTAapqa5K3Ade0cW+tqq3t+auBDwH7Ap9pf5KkgSx62FTV/2H28yoAx8wyvoDT53ivdcC6WeobgWfvRJuSpAXkFQQkSd0NcRhNU2D52suHbkHSbsQ9G0lSd4aNJKk7w0aS1J1hI0nqzrCRJHVn2EiSujNsJEndGTaSpO4MG0lSd4aNJKk7w0aS1J1hI0nqzrCRJHVn2EiSujNsJEndGTaSpO4MG0lSd4aNJKk7w0aS1J1hI0nqzrCRJHVn2EiSujNsJEnd7TV0A5K0reVrLx9s27eedcJg255m7tlIkrozbCRJ3Rk2kqTuDBtJUndTO0EgySrgvcAS4INVddbALS24IU+iStKjMZV7NkmWAO8HjgMOA16R5LBhu5KkPddUhg1wJLCpqm6pqgeBi4GTBu5JkvZY03oY7WDg9rHlzcDzB+pF0m5kqMPT0/77nmkNm8xSq0cMStYAa9ri95N8q2NPBwH/2PH9dyd+FyN+Dw/b47+LvBPYPb+Hp08yaFrDZjNwyNjyMuCObQdV1XnAeYvRUJKNVbVyMba1q/O7GPF7eJjfxcg0fw/Tes7mGmBFkkOT7A2cDFw2cE+StMeayj2bqnooyWuA9YymPq+rqhsHbkuS9lhTGTYAVXUFcMXQfYxZlMN1uwm/ixG/h4f5XYxM7feQqkecN5ckaUFN6zkbSdIuxLAZQJI3JqkkBw3dy1CS/HmSbyb5epL/meSAoXtaTElWJflWkk1J1g7dzxCSHJLk80luSnJjktcN3dOQkixJ8tUkfzt0Lz0YNossySHAi4Dbhu5lYBuAZ1fVrwH/F3jTwP0sGi+n9DMPAW+oql8GjgJO30O/hxmvA24auoleDJvFdzbwx8zyI9M9SVX9XVU91Ba/zOi3UHsKL6cEVNWdVfWV9vw+Rv/QHjxsV8NIsgw4Afjg0L30YtgsoiQnAt+pqq8N3csu5veAzwzdxCKa7XJKe+Q/sjOSLAcOB64atpPBvIfR/4T+dOhGepnaqc9DSfJZ4MmzrHoL8Gbg2MXtaDjzfRdVdWkb8xZGh1MuWszeBjbR5ZT2FEl+HvgE8PqqunfofhZbkpcAd1XVtUl+a+h+ejFsFlhVvXC2epJfBQ4FvpYERoeNvpLkyKr6h0VscdHM9V3MSLIaeAlwTO1Zc/AnupzSniDJYxkFzUVV9cmh+xnI0cCJSY4H9gH2T/LXVfUfB+5rQfk7m4EkuRVYWVW720X3FkS7ud27gd+sqi1D97OYkuzFaFLEMcB3GF1e6ZV72lUuMvq/rguArVX1+qH72RW0PZs3VtVLhu5loXnORkN5H/ALwIYk1yX5i6EbWixtYsTM5ZRuAi7Z04KmORr4XeAF7b+B69r/3WsKuWcjSerOPRtJUneGjSSpO8NGktSdYSNJ6s6wkSR1Z9hIu6gky5PcMHQf0kIwbCRJ3Rk20m4gyTPavU6eN3Qv0o4wbKRdXJJnMbp+2KlVdc3Q/Ug7wgtxSru2pcClwL/fQy9poynhno20a7uH0b1vjh66EWlnuGcj7doeBF4GrE/y/ar6yNANSTvCsJF2cVV1f7vB1oYk98/ceE7anXjVZ0lSd56zkSR1Z9hIkrozbCRJ3Rk2kqTuDBtJUneGjSSpO8NGktSdYSNJ6u7/A9h7VuctvsAWAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(rayleigh_sample)\n",
    "\n",
    "plt.xlabel(\"k\")\n",
    "\n",
    "plt.ylabel(\"Frequency (X=k)\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Pandas\n",
    "\n",
    "Pandas is a data analytics and a data processing library.\n",
    "\n",
    "In Pandas, the data gets stored as a new kind of a data structure.\n",
    "\n",
    "In python the data structures are:\n",
    "\n",
    "1.List \n",
    "\n",
    "2.Dictionary - Associative Array.\n",
    " \n",
    "3.Tuple \n",
    "\n",
    "4.Set \n",
    "\n",
    "5.Numpy Arrays - supports matrix calculation and linear algebra calculation.\n",
    "\n",
    "6.Pandas dataframe - statistical analysis and probability \n",
    "\n",
    "7.Scipy - Differential Calculas. \n",
    "\n",
    "Every data structure provide some way to access the data. Which is different for every data structure."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "# To read the data file for pandas, know as pandas Dataframe\n",
    "#data = pd.read_csv(\"file name\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To convert the data frame into a numpy array"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "#data_np_array = "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "#data.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}