DataScience365/Day-13/Probability Distributions part-2.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# `Probability Distributions`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline \n",
    "# for inline plots in jupyter\n",
    "import matplotlib.pyplot as plt# import matplotlib\n",
    "import seaborn as sns\n",
    "import warnings\n",
    "warnings.simplefilter(\"ignore\")\n",
    "from ipywidgets import interact"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "styles = ['seaborn-notebook', 'seaborn', 'seaborn-darkgrid', 'classic', \n",
    "          '_classic_test', 'seaborn-poster', 'tableau-colorblind10', 'grayscale', \n",
    "          'fivethirtyeight', 'seaborn-ticks', 'seaborn-dark', \n",
    "          'dark_background', 'seaborn-pastel', \n",
    "          'fast', 'Solarize_Light2', 'seaborn-colorblind', 'seaborn-white',\n",
    "          'seaborn-dark-palette',\n",
    "          'bmh', 'seaborn-talk', 'seaborn-paper', 'seaborn-deep', 'seaborn-bright', \n",
    "          'seaborn-muted', \n",
    "          'seaborn-whitegrid', 'ggplot']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## `3. Bernoulli Distribution`\n",
    "A random variable X is said to be a Bernoulli random variable with parameter p, shown as X∼Bernoulli(p), if its PMF is given by\n",
    "\n",
    "\\begin{equation}\n",
    "             \\nonumber P_X(x) = \\left\\{\n",
    "              \\begin{array}{l l}\n",
    "                 p& \\quad \\text{for  } x=1\\\\\n",
    "                1-p & \\quad \\text{ for } x=0\\\\\n",
    "                0  & \\quad \\text{ otherwise}\n",
    "              \\end{array} \\right.\n",
    "            \\end{equation}\n",
    "\n",
    "            where 0<p<1.\n",
    "![](http://probabilitycourse.com/images/chapter3/bernoulli(p)%20color.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# import bernoulli\n",
    "from scipy.stats import bernoulli"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Bernoulli random variable can take either 0 or 1 using certain probability as a parameter. To generate 10000, bernoulli random numbers with success probability p =0.3, we will use bernoulli.rvs with two arguments."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Text(0,0.5,'Frequency'), Text(0.5,0,'Bernoulli')]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# generate bernoulli\n",
    "data_bern = bernoulli.rvs(size=10000,p=0.3)\n",
    "ax= sns.distplot(data_bern,\n",
    "                 kde=False,\n",
    "                 hist_kws={\"linewidth\": 15,'alpha':1})\n",
    "ax.set(xlabel='Bernoulli', ylabel='Frequency')\n",
    "# We can see from the plot below out of 10000 trials with success probability 0.3, \n",
    "# we get about 3000 successes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def BernoulliDistribution(palette=\"dark\",kde = False,style = \"ggplot\"):\n",
    "    plt.figure(figsize=(13,10))\n",
    "    plt.style.use(style)\n",
    "    sns.set_palette(palette)\n",
    "    ax= sns.distplot(data_bern,\n",
    "                 kde=kde,\n",
    "                 hist_kws={\"linewidth\": 15,'alpha':1})\n",
    "    ax.set(xlabel='Bernoulli', ylabel='Frequency')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "389a8d0298704e8d931baed95cec8508",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(Dropdown(description='palette', index=4, options=('deep', 'muted', 'pastel', 'bright', '…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "interact(BernoulliDistribution,palette = [\"deep\", \"muted\", \"pastel\", \"bright\", \n",
    "                    \"dark\", \"colorblind\",\"Set3\",\"Set2\"],kde = [True,False],style = styles);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## `4. Binomial Distribution`\n",
    "\n",
    "1. The binomial distribution is a discrete probability distribution that gives the probability that n identical independently distributed Bernoulli trials sum to k, where n is any natural number.\n",
    "![](https://www.s-cool.co.uk/gifs/a-mat-sdisc-dia08.gif)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import binom"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Binomial distribution is a discrete probability distributionlike Bernoulli. It can be used to obtain the number of successes from N Bernoulli trials. For example, to find the number of successes in 10 Bernoulli trials with p =0.5, we will use"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "binom.rvs(n=10,p=0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* We can also use binom.rvs to repeat the trials with size argument. If we want to repeat 5 times, we will use"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Text(0,0.5,'Frequency'), Text(0.5,0,'Binomial')]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data_binom = binom.rvs(n=10,p=0.5,size=10000)\n",
    "ax = sns.distplot(data_binom,\n",
    "                  kde=False,\n",
    "                  hist_kws={\"linewidth\": 15,'alpha':1})\n",
    "ax.set(xlabel='Binomial', ylabel='Frequency')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def BinomialDistribution(palette=\"dark\",kde = False,style = \"ggplot\"):\n",
    "    plt.figure(figsize=(13,10))\n",
    "    plt.style.use(style)\n",
    "    sns.set_palette(palette)\n",
    "    ax = sns.distplot(data_binom,\n",
    "                  kde=kde,\n",
    "                  hist_kws={\"linewidth\": 15,'alpha':1})\n",
    "    ax.set(xlabel='Binomial', ylabel='Frequency')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "1eadb342572c4d19ad2075ce5de5cdbd",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(Dropdown(description='palette', index=4, options=('deep', 'muted', 'pastel', 'bright', '…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "interact(BinomialDistribution,palette = [\"deep\", \"muted\", \"pastel\", \"bright\", \n",
    "                    \"dark\", \"colorblind\",\"Set3\",\"Set2\"],kde = [True,False],style = styles);"
   ]
  }
 ],
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