Module 001.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Python"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "ls = [1, 2, 3, 4]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n",
      "2\n",
      "3\n",
      "4\n"
     ]
    }
   ],
   "source": [
    "for i in ls:\n",
    "    print(i)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def odd_even(_ls):\n",
    "    for i in ls:\n",
    "        if i % 2 == 0:\n",
    "            print(\"{%d} is even\" % i)\n",
    "        else:\n",
    "            print(\"{%d} is odd\" % i)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{1} is odd\n",
      "{2} is even\n",
      "{3} is odd\n",
      "{4} is even\n"
     ]
    }
   ],
   "source": [
    "odd_even(ls)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def square_it(x):\n",
    "    return x**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 4, 9, 16]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[square_it(i) for i in ls]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Math:\n",
    "    def __init__(self):\n",
    "        pass\n",
    "    \n",
    "    @staticmethod\n",
    "    def operation():\n",
    "        pass\n",
    "    \n",
    "    def __str__(self):\n",
    "        return \"Math Class\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Square(Math):\n",
    "    def __init__(self):\n",
    "        super(Square, self).__init__()\n",
    "        \n",
    "    @staticmethod\n",
    "    def operation(operand):\n",
    "        return operand ** 2\n",
    "    \n",
    "    def __str__(self):\n",
    "        ret = super(Square, self).__str__()\n",
    "        return ret + \"\\nSquare Operation\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<__main__.Square at 0x7f6baf746080>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Square()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "obj = Square()\n",
    "obj.operation(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Square.operation(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Math Class\n"
     ]
    }
   ],
   "source": [
    "obj_math = Math()\n",
    "print(obj_math)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Math Class\n",
      "Square Operation\n"
     ]
    }
   ],
   "source": [
    "obj_sqrit = Square()\n",
    "print(obj_sqrit)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Zero in Python"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = -0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = +0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x == y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Infinity in Python"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = 1e10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = 1e20"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0000000001e+20"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x+y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "z = 1e1000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "inf"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x*y*z"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Nan in Python"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'inf' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-22-dc0e8e901507>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mx\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0minf\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m: name 'inf' is not defined"
     ]
    }
   ],
   "source": [
    "x = inf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "from numpy import sqrt, inf, isnan, nan"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/qamaruddin/anaconda3/lib/python3.6/site-packages/ipykernel_launcher.py:1: RuntimeWarning: invalid value encountered in sqrt\n",
      "  \"\"\"Entry point for launching an IPython kernel.\n"
     ]
    }
   ],
   "source": [
    "y = sqrt(-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "nan"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "nan"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x+y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x == y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "isnan(x+y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Catastrophic Cancellation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "epsilon = 1e-1000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "epsilon"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = 101"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = x + epsilon"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x == y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Avoid subtracting two nearly-equal numbers.\n",
    "\n",
    "* Especially in a loop!\n",
    "\n",
    "* Better-yet use a well-validated existing implementation in the form of a numerical library."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Numpy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 3, 4])"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.array([1, 2, 3, 4])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27,\n",
       "       28, 29, 30, 31, 32])"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.array(np.arange(11, 33))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27,\n",
       "       28, 29, 30, 31, 32])"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.arange(11, 33)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "907"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.randint(low=0, high=1e3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "44"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.randint(low=0, high=1e3, size=None)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(seed=101)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "863"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.randint(low=0, high=1e3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "523"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.randint(low=0, high=1e3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[337, 838, 575, 599],\n",
       "       [ 75, 393, 973, 552],\n",
       "       [644, 575, 936, 757]])"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.randint(low=0, high=1e3, size=(3,4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.8480769834036315"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.normal()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5542275911247871"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.uniform()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-4.394034650505066"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.normal(loc=-5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-3.9948622133625764"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.normal(scale=3.7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-6.856958068158365"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.normal(loc=-5, scale=3.7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.random.normal(size=(3,4))\n",
    "y = np.random.uniform(size=(4,2))\n",
    "\"\"\"\n",
    "df :\n",
    "    float or array_like of floats\n",
    "    Number of degrees of freedom, should be > 0.\n",
    "\"\"\"\n",
    "z = np.random.chisquare(df=1, size=(3,3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "operands could not be broadcast together with shapes (3,4) (4,2) ",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-50-cd60f97aa77f>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mx\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m: operands could not be broadcast together with shapes (3,4) (4,2) "
     ]
    }
   ],
   "source": [
    "x + y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.16814492, -0.10806726,  1.51144365,  0.68346094],\n",
       "       [ 0.93991936, -1.1349718 , -0.63579197,  0.02515971],\n",
       "       [-0.27306951, -0.31589962,  0.00858304,  0.20530702]])"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.57878954, 0.73481906],\n",
       "       [0.54196177, 0.91315356],\n",
       "       [0.80792015, 0.40299783],\n",
       "       [0.35722434, 0.95287671]])"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.23616532, 2.16412486, 0.02115521],\n",
       "       [3.17142043, 0.15188046, 0.05399103],\n",
       "       [0.47557622, 0.1002952 , 0.02900853]])"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.33628985, -0.21613451,  3.0228873 ,  1.36692188],\n",
       "       [ 1.87983872, -2.26994359, -1.27158394,  0.05031941],\n",
       "       [-0.54613902, -0.63179924,  0.01716608,  0.41061404]])"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x + x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.83185508,  0.89193274,  2.51144365,  1.68346094],\n",
       "       [ 1.93991936, -0.1349718 ,  0.36420803,  1.02515971],\n",
       "       [ 0.72693049,  0.68410038,  1.00858304,  1.20530702]])"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x + 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-1.16814492, -1.10806726,  0.51144365, -0.31653906],\n",
       "       [-0.06008064, -2.1349718 , -1.63579197, -0.97484029],\n",
       "       [-1.27306951, -1.31589962, -0.99141696, -0.79469298]])"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x - 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.33628985, -0.21613451,  3.0228873 ,  1.36692188],\n",
       "       [ 1.87983872, -2.26994359, -1.27158394,  0.05031941],\n",
       "       [-0.54613902, -0.63179924,  0.01716608,  0.41061404]])"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x * 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2.82727151e-02, 1.16785317e-02, 2.28446191e+00, 4.67118858e-01],\n",
       "       [8.83448400e-01, 1.28816098e+00, 4.04231432e-01, 6.33010847e-04],\n",
       "       [7.45669581e-02, 9.97925684e-02, 7.36686006e-05, 4.21509730e-02]])"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x ** 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "12"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3, 4)"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/qamaruddin/anaconda3/lib/python3.6/site-packages/ipykernel_launcher.py:1: RuntimeWarning: invalid value encountered in sqrt\n",
      "  \"\"\"Entry point for launching an IPython kernel.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[       nan,        nan, 1.22940785, 0.82671697],\n",
       "       [0.96949438,        nan,        nan, 0.15861812],\n",
       "       [       nan,        nan, 0.09264471, 0.45310818]])"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sqrt(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/qamaruddin/anaconda3/lib/python3.6/site-packages/ipykernel_launcher.py:1: RuntimeWarning: invalid value encountered in sqrt\n",
      "  \"\"\"Entry point for launching an IPython kernel.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[0.        , 0.        , 1.22940785, 0.82671697],\n",
       "       [0.96949438, 0.        , 0.        , 0.15861812],\n",
       "       [0.        , 0.        , 0.09264471, 0.45310818]])"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res = np.sqrt(x)\n",
    "np.nan_to_num(res)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.84523133, 0.89756723, 4.53327053, 1.98072104],\n",
       "       [2.55977499, 0.32143119, 0.52951596, 1.02547888],\n",
       "       [0.76103988, 0.72913264, 1.00861998, 1.227902  ]])"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.exp(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.80649842e-08, 2.17240712e-10, 6.22185097e+01, 2.22401136e-02],\n",
       "       [5.38153221e-01, 3.54691429e+00, 1.07932044e-02, 1.01637918e-16],\n",
       "       [2.30532486e-06, 9.89671358e-06, 2.16976201e-21, 1.33057090e-07]])"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x ** 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.30938582,  1.03812444],\n",
       "       [-0.57577732, -0.57798156],\n",
       "       [-0.24898021, -0.29003031]])"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.matmul(x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.30938582,  1.03812444],\n",
       "       [-0.57577732, -0.57798156],\n",
       "       [-0.24898021, -0.29003031]])"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.dot(x, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "matmul differs from dot in two important ways.\n",
    "\n",
    "* Multiplication by scalars is not allowed.\n",
    "* Stacks of matrices are broadcast together as if the matrices were elements."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.        ,  1.47368421,  1.94736842,  2.42105263,  2.89473684,\n",
       "        3.36842105,  3.84210526,  4.31578947,  4.78947368,  5.26315789,\n",
       "        5.73684211,  6.21052632,  6.68421053,  7.15789474,  7.63157895,\n",
       "        8.10526316,  8.57894737,  9.05263158,  9.52631579, 10.        ])"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linspace(1, 10, 20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Matplotlib"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.2299375 , -1.28359884, -2.71119174, -1.52241044, -1.41620705,\n",
       "        1.10854366,  1.13102858,  0.49860031,  1.17902193,  1.32268437,\n",
       "        1.85215451, -0.89217198,  0.61686071, -1.121822  ,  1.65207044,\n",
       "        0.19692527,  0.10321419, -0.14737026,  1.13128366,  1.08583909,\n",
       "        0.44948591, -0.00296292, -0.64817706, -0.95614981,  1.61046122,\n",
       "        1.31961786, -0.36370359,  1.08173118,  1.77565169,  0.43574312,\n",
       "        1.19499883,  1.07654708, -0.98177   , -1.765463  , -0.75843621,\n",
       "       -0.45469606,  1.29761741, -0.82537764,  0.25191495,  0.51876342,\n",
       "        0.58796761, -0.14819361, -0.87670184,  0.79275011,  0.53911754,\n",
       "        0.66977395, -1.27048376, -0.44618085,  0.77947505,  0.47989973,\n",
       "       -0.96069741, -2.0023987 , -1.26359946, -0.69623188, -1.14821996,\n",
       "        1.60743482, -1.22686962,  1.40553189, -1.13720133, -0.53547812,\n",
       "        2.14271732,  1.6914524 ,  0.27522457, -0.85205693,  0.29865904,\n",
       "       -0.56537013,  0.3583247 ,  0.69967642,  0.41736607, -0.23804927,\n",
       "       -1.85003782,  1.04977352, -0.43786985,  0.60833433, -0.34202133,\n",
       "        0.58901967,  0.82738787,  0.16304364,  0.03136322,  0.78310514,\n",
       "        0.06956025,  0.66013576,  0.8113491 , -1.29979434,  2.19524927,\n",
       "       -0.6202431 , -1.53176856,  0.06199649,  0.82312181,  0.6441213 ,\n",
       "       -0.37370039,  0.71307312, -0.75606407,  0.19907613,  0.97918106,\n",
       "       -0.56119837,  0.54383269,  0.24829089, -1.15203651, -0.31688706])"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.normal(size=(100,))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = np.random.normal(size=(100,))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f6b9fdcbdd8>]"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6b9fe73780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f6b9fd5dc50>]"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6b9fe22390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.arange(0, 100)\n",
    "y = data\n",
    "plt.plot(x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f6b9fcc0ac8>]"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6b9fd3a2e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.arange(0, 100)\n",
    "y = data\n",
    "plt.plot(y, x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6b9fcffac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(y, x)\n",
    "plt.xlim(-5, 5)\n",
    "plt.xlabel('Range')\n",
    "plt.ylabel('Domain')\n",
    "plt.title('Normal Random')\n",
    "plt.grid(True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gaussian_distribution(x, meu=0, sigma=1):\n",
    "    return np.exp((-1*((x-meu)**2)/(2*sigma**2)))/np.sqrt(2*np.pi*(sigma**2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.141592653589793"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.pi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7.69459862670642e-23"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gaussian_distribution(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.arange(0, 10, 2)\n",
    "y = [gaussian_distribution(i) for i in x]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 2, 4, 6, 8])"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0.3989422804014327,\n",
       " 0.05399096651318806,\n",
       " 0.00013383022576488537,\n",
       " 6.075882849823286e-09,\n",
       " 5.052271083536893e-15]"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3.98942280e-01, 5.39909665e-02, 1.33830226e-04, 6.07588285e-09,\n",
       "       5.05227108e-15])"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "meu = 0\n",
    "sigma = 1\n",
    "np.exp(-1*((x - meu)**2) / (2*sigma**2))/np.sqrt(2*np.pi*sigma**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f6b9fc047b8>]"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6b9fcff128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = [gaussian_distribution(i, meu=4, sigma=1.3) for i in x]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f6b9fbf6080>]"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6b9fc30470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.arange(0, 10.1, 0.1)\n",
    "y = [gaussian_distribution(i, meu=5, sigma=1.1) for i in x]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6b9fbcfd68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, y)\n",
    "plt.grid(True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.44399364, 0.63237388, 0.28581935, 0.60864697, 0.68533024,\n",
       "       0.82047921, 0.31259461, 0.28086754, 0.29738297, 0.44765589])"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.uniform(size=(10))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "plot takes an argument fmt of the following signature\n",
    "fmt = '[color][marker][line]'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f6b9fb6f048>]"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6b9fba63c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data = np.random.uniform(low=0, high=10, size=(10))\n",
    "plt.plot(data, \"ro--\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([2, 2, 0, 0, 2, 0, 2, 0, 0, 2]),\n",
       " array([1.22970899, 2.0813644 , 2.93301981, 3.78467522, 4.63633063,\n",
       "        5.48798604, 6.33964145, 7.19129686, 8.04295227, 8.89460768,\n",
       "        9.74626309]))"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.histogram(np.random.uniform(low=0, high=10, size=(10)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 1, 0, 1, 1, 1, 0, 1, 0, 4])"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = np.random.uniform(low=0, high=10, size=(10))\n",
    "hist, bins = np.histogram(data)\n",
    "hist"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.26691995, 2.07922852, 2.8915371 , 3.70384568, 4.51615426,\n",
       "       5.32846284, 6.14077142, 6.95308   , 7.76538857, 8.57769715,\n",
       "       9.39000573])"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bins"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f6b9fcb61d0>]"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6b9faff780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(hist)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [],
   "source": [
    "hist, bins = np.histogram(data, bins=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f6b9fabf160>]"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6b9fc8c0b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(hist)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Container object of 10 artists>"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6b9fb782e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.bar(hist, height=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6b9fad6da0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n, bins, patches = plt.hist(data, bins=10, normed=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7f6b9f98b9b0>"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6b9fa20ac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import time\n",
    "%matplotlib inline\n",
    "\n",
    "np.random.seed(seed=int(time.time()))\n",
    "x = np.random.normal(size=(10, 10))\n",
    "y = np.random.normal(size=(10, 10))\n",
    "z = np.random.randint(0, 2, size=(10, 10))\n",
    "plt.scatter(x, y, c=z, label=z, cmap=\"cool\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Scipy Stats"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* See Lecture Notes:\n",
    "    * probability mass function\n",
    "    * probability density function\n",
    "    * cumulative distribution function\n",
    "    * percntile point function\n",
    "    * degrees of freedom, moments, skew, kurtosis\n",
    "    * genrating functions\n",
    "    * correlation\n",
    "    * variance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy import stats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-2.3263478740408408"
      ]
     },
     "execution_count": 100,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.norm.ppf(0.01)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.3263478740408408"
      ]
     },
     "execution_count": 101,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.norm.ppf(0.99)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-2.32634787,  2.32634787])"
      ]
     },
     "execution_count": 102,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.norm.ppf([0.01, 0.99])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-2.32634787,  0.        ,  2.32634787])"
      ]
     },
     "execution_count": 103,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.norm.ppf([0.01, 0.5, 0.99])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-2.32634787, -2.27935095, -2.23235402, -2.18535709, -2.13836017,\n",
       "       -2.09136324, -2.04436631, -1.99736939, -1.95037246, -1.90337553,\n",
       "       -1.85637861, -1.80938168, -1.76238475, -1.71538783, -1.6683909 ,\n",
       "       -1.62139397, -1.57439705, -1.52740012, -1.48040319, -1.43340627,\n",
       "       -1.38640934, -1.33941241, -1.29241549, -1.24541856, -1.19842163,\n",
       "       -1.15142471, -1.10442778, -1.05743085, -1.01043393, -0.963437  ,\n",
       "       -0.91644007, -0.86944314, -0.82244622, -0.77544929, -0.72845236,\n",
       "       -0.68145544, -0.63445851, -0.58746158, -0.54046466, -0.49346773,\n",
       "       -0.4464708 , -0.39947388, -0.35247695, -0.30548002, -0.2584831 ,\n",
       "       -0.21148617, -0.16448924, -0.11749232, -0.07049539, -0.02349846,\n",
       "        0.02349846,  0.07049539,  0.11749232,  0.16448924,  0.21148617,\n",
       "        0.2584831 ,  0.30548002,  0.35247695,  0.39947388,  0.4464708 ,\n",
       "        0.49346773,  0.54046466,  0.58746158,  0.63445851,  0.68145544,\n",
       "        0.72845236,  0.77544929,  0.82244622,  0.86944314,  0.91644007,\n",
       "        0.963437  ,  1.01043393,  1.05743085,  1.10442778,  1.15142471,\n",
       "        1.19842163,  1.24541856,  1.29241549,  1.33941241,  1.38640934,\n",
       "        1.43340627,  1.48040319,  1.52740012,  1.57439705,  1.62139397,\n",
       "        1.6683909 ,  1.71538783,  1.76238475,  1.80938168,  1.85637861,\n",
       "        1.90337553,  1.95037246,  1.99736939,  2.04436631,  2.09136324,\n",
       "        2.13836017,  2.18535709,  2.23235402,  2.27935095,  2.32634787])"
      ]
     },
     "execution_count": 104,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linspace(stats.norm.ppf(0.01), stats.norm.ppf(0.99), 100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<scipy.stats._distn_infrastructure.rv_frozen at 0x7f6b97f81828>"
      ]
     },
     "execution_count": 105,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.norm()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.02665214, 0.0296985 , 0.03302004, 0.03663206, 0.04054955,\n",
       "       0.04478694, 0.049358  , 0.05427559, 0.05955143, 0.06519596,\n",
       "       0.07121803, 0.0776247 , 0.08442105, 0.09160987, 0.09919153,\n",
       "       0.1071637 , 0.11552116, 0.12425566, 0.13335569, 0.14280642,\n",
       "       0.1525895 , 0.16268307, 0.17306164, 0.18369615, 0.19455396,\n",
       "       0.20559893, 0.21679157, 0.22808919, 0.23944611, 0.25081392,\n",
       "       0.26214179, 0.2733768 , 0.28446433, 0.29534848, 0.30597253,\n",
       "       0.3162794 , 0.32621215, 0.33571453, 0.34473146, 0.35320956,\n",
       "       0.36109774, 0.3683476 , 0.37491403, 0.38075561, 0.38583507,\n",
       "       0.39011967, 0.39358159, 0.39619817, 0.39795222, 0.39883215,\n",
       "       0.39883215, 0.39795222, 0.39619817, 0.39358159, 0.39011967,\n",
       "       0.38583507, 0.38075561, 0.37491403, 0.3683476 , 0.36109774,\n",
       "       0.35320956, 0.34473146, 0.33571453, 0.32621215, 0.3162794 ,\n",
       "       0.30597253, 0.29534848, 0.28446433, 0.2733768 , 0.26214179,\n",
       "       0.25081392, 0.23944611, 0.22808919, 0.21679157, 0.20559893,\n",
       "       0.19455396, 0.18369615, 0.17306164, 0.16268307, 0.1525895 ,\n",
       "       0.14280642, 0.13335569, 0.12425566, 0.11552116, 0.1071637 ,\n",
       "       0.09919153, 0.09160987, 0.08442105, 0.0776247 , 0.07121803,\n",
       "       0.06519596, 0.05955143, 0.05427559, 0.049358  , 0.04478694,\n",
       "       0.04054955, 0.03663206, 0.03302004, 0.0296985 , 0.02665214])"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.linspace(stats.norm.ppf(0.01), stats.norm.ppf(0.99), 100)\n",
    "frozen_norm = stats.norm()\n",
    "frozen_norm.pdf(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,1,'Normal Distribution')"
      ]
     },
     "execution_count": 107,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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n4xg/Iqq+9edhUlKSJicnOx3DOCjryDGGPPMdnVrUZ/rYkwNi9MzqkHkgh2HPLiQptglvXdfX/hoKciKyVFWTypvPrsg1Puehz1PIzS/i8Qu7W+H/gTaN63DP8E4s3JDFZyvsoi3jGSt941Pmr9vNl6t2cvtZHekQVc/pOD7vqlNi6d22EQ9/nsKB7Hyn4xg/YKVvfEZufhETZ6YQ37weY0/r4HQcvxAaIvzzgh4czitk8uz1TscxfsBK3/iMKd+mkXkgl3+c342IMPvR9FSnlvW54dQ43v8lg2XbDjgdx/g4+80yPmFT1lGmLtzEBX2i6d8+cMfIry53nBVPywaRPPDJGgqL7BaL5sSs9I3jVJUHP1tD7fBQ/j6yi9Nx/FLdWmFMPC+RtTsP2xAN5g9Z6RvHfbFqJz+m7ePu4Z2Iql/L6Th+a0S3lpyWEMXTczaw53Ce03GMj7LSN47KyS/ksa/W0bV1Ay7v387pOH5NRHh4VFeOFRbxxNepTscxPspK3zjq5QWb2Hkoj4dGdQ3qETS9Ja5ZXa4/NY6PlmWy3A7qmjJY6RvHZOzPYerCdEb1bE3fILwxSnW57cx4ourX4qHP19q4++Z3rPSNYx77ah0hIvz97M5ORwko9WqFMWFEZ1ZmHOTj5dudjmN8jJW+ccSitL3MWrOLW8/oQKuGNqCat/2pdzS9YhrxxNfrOXqs0Ok4xodY6ZsaV1SsTPpiLW0a1+bGQe2djhOQQkKEh0Z1JevIMf69IM3pOMaHWOmbGvfR0kzW7zrChJGdiQwPdTpOwOoV04jze7Xm1e83283Uza+s9E2Nyj5WyJNzUunTthHndG/ldJyAd/eIkuMlT35t4/KYElb6pkZN/W4TWUeO8cC5iTb+ew2IblSbPw9qz6crdrAi46DTcYwPsNI3NWbHwVymfZ/OeT1b06dtY6fjBI2bB3egWb1a/OOLtfjaTZNMzbPSNzXmqTmpFCvcM7yT01GCSr1aYdw1LIHkrQf4es0up+MYh3lU+iIyQkRSRSRNRCaU8frNIrJaRFaIyA8ikuj22t9dy6WKyHBvhjf+Y+2Ow3yyfDvXDYglpkkdp+MEnYtPakN883pMnp1KgY3CGdTKLX0RCQWmACOBROAy91J3eU9Vu6tqL2Ay8Ixr2URgDNAVGAG85FqfCTL//Ho9DSLDuWVwR6ejBKWw0BAmjOzM5r3ZTP9lm9NxjIM82dLvB6Sparqq5gPTgdHuM6jqYbendYHjOw5HA9NV9ZiqbgbSXOszQeTHtL0s3JDFuDM60rBOuNNxgtaZnZvTL64Jz8/faBdsBTFPSj8ayHB7numa9hsicquIbKJkS//2Ci47VkSSRSQ5KyvL0+zGDxQXK4/PWkd0o9pcdYqNoukkEeG+s7uw92g+ryxMdzqOcYgnpV/WeXW/OwVAVaeoagfgXuCBCi47TVWTVDUpKirKg0jGX3y+agdrth/mb8MT7EIsH9ArpuT6iFe+T2fPERtzPxh5UvqZQIzb8zbAjj+YfzpwfiWXNQEkv7CYp+akktiqAaN7/u4PPOOQu4d3Ir+wmBfm2/AMwciT0l8CxItInIhEUHJgdqb7DCIS7/b0HGCj6/FMYIyI1BKROCAe+KXqsY0/mL5kGxn7c7lnRCdCbKx8nxHbrC5j+sXw/i/b2Lov2+k4poaVW/qqWgiMA2YD64APVDVFRCaJyCjXbONEJEVEVgDjgWtcy6YAHwBrga+BW1W1qBq+D+Njso8V8q/5afSPa8LpCbbLztfcfmY8YaHCM3M3OB3F1LAwT2ZS1a+Ar0pNe9Dt8R1/sOyjwKOVDWj80xs/bmbv0WNMveokG27BBzVvEMn1A+N4acEmxp7Wnq6tGzodydQQuyLXeN2B7HymfpfO0MQWnNTOhlvwVTed3oGGtcN5crbdTzeYWOkbr/v3d5vIzi/kbhtuwac1rB3OLYM7sCA1i5/T9zkdx9QQK33jVbsO5fHWoi2c3zuahBb1nY5jynHNgFhaNKjFU7NTbTC2IGGlb7zqhW82UqzKX4ckOB3FeCAyPJTbzowneesBFqTahZHBwErfeM22fTn8d0kGY/q2tUHV/MglSTHENKldMgpqsW3tBzorfeM1z83bQFiocNuZNqiaP4kIC+GvQxJI2XGYWTb0csCz0jdesWH3ET5ZsZ1rTomleYNIp+OYChrdK5r45vV4Zm4qhTb0ckCz0jde8cycDdSNCOPm0zs4HcVUQmiIcNewBDZlZfPJ8u1OxzHVyErfVNnqzEN8nbKLG06No3HdCKfjmEoa3rUl3aMb8q9vNpJfaFv7gcpK31TZM3NTaVQnnBsGxTkdxVSBiDB+WAIZ+3P5cGlG+QsYv2Slb6pk6db9fJuaxU2ndaBBpN0gxd8NTojipHaNeWF+GnkFNkxWILLSN1Xy9JwNNKsXwTUD7AYpgUCkZN/+rsN5vLfYbqsYiKz0TaUtStvLok37uGVwR+pEeDR2n/EDAzo0Y0CHpry0II2cfLutYqCx0jeVoqo8PXcDLRtEcnn/tk7HMV5217AE9h7N581FW5yOYrzMSt9UyoINWSzdeoBxZ3a02yAGoJPaNWFwpyimLUznSF6B03GMF1npmwpTVZ6du4E2jWtzSVJM+QsYvzR+aAIHcwp448ctTkcxXmSlbyps3ro9rMo8xO1nxhMRZj9CgapHm0YMTWzBK9+ncyjHtvYDhUe/sSIyQkRSRSRNRCaU8fp4EVkrIqtEZL6ItHN7rUhEVri+ZpZe1viX4mLlmbkbiG1ahwv62M3OA934oQkcySvk1R/SnY5ivKTc0heRUGAKMBJIBC4TkcRSsy0HklS1BzADmOz2Wq6q9nJ9jcL4ta9TdrFu52HuGBJPWKht5Qe6Lq0acE73Vrz+w2b2Z+c7Hcd4gSe/tf2ANFVNV9V8YDow2n0GVf1WVXNcT38G2ng3pvEFRcXKc/M20CGqLqN62lZ+sLhzSDw5BUVMXbjJ6SjGCzwp/WjA/ZrsTNe0E7kBmOX2PFJEkkXkZxE5v6wFRGSsa57krCy7kYOv+mLVDjbsPsqdQxIIDbGbnQeL+Bb1GdWzNf9ZtJWsI8ecjmOqyJPSL+u3u8w7LYjIlUAS8KTb5LaqmgRcDjwnIr8bhlFVp6lqkqomRUVFeRDJ1LTComKen7eRTi3qc073Vk7HMTXsjrPiOVZYxNTvbGvf33lS+pmA+3l5bYAdpWcSkSHA/cAoVf11c0BVd7j+mw4sAHpXIa9xyMyVO0jfm81fh8YTYlv5Qad9VD3+1LsNb/+8lT2H85yOY6rAk9JfAsSLSJyIRABjgN+chSMivYGplBT+HrfpjUWklutxM2AgsNZb4U3NKCgq5vn5G0ls1YBhiS2djmMccvtZHSksVl5aYFv7/qzc0lfVQmAcMBtYB3ygqikiMklEjp+N8yRQD/iw1KmZXYBkEVkJfAv8U1Wt9P3MJ8u2s3VfDuOHJthWfhBr17QuF5/UhvcWb2PnoVyn45hKElXfuhFyUlKSJicnOx3DuOQXFnPm0wtoUjeCz24diIiVfjDL2J/DmU8v4JKkGB79U3en4xg3IrLUdfz0D9mJ1uYPfbg0g8wDufx1aIIVviGmSR0uSYrhg+QMMvbnlL+A8TlW+uaE8gqKePGbNPq0bcTgBDurypQYd2ZHBOHFb9KcjmIqwUrfnNB/l2Sw81Ae44d2sq1886tWDWtzef+2zFiWydZ92U7HMRVkpW/KlFdQxJRv0+gX14SBHZs6Hcf4mFsGdyAsRHh+/kano5gKstI3ZXrn563sOXKM8bYv35SheYNIrjq5HZ8u386mrKNOxzEVYKVvficnv5CXv9vEwI5NObm9beWbst08uAO1wkJ5fp5t7fsTK33zO28t2sreo/mMH5rgdBTjw5rVq8U1A2L5fNUOUncdcTqO8ZCVvvmNI3kFTF24idMTojipXROn4xgfd9Np7akbEcZz8zY4HcV4yErf/MYbP27hYE6BbeUbjzSuG8H1A2OZtWYXKTsOOR3HeMBK3/zqUE4Br3yfzpAuLegZ08jpOMZP3DCoPQ0iw3h2rm3t+wMrffOrV39I50heoW3lmwppWDucsae1Z966PazIOOh0HFMOK30DwP7sfF7/YTPndG9FYusGTscxfubagXE0rhPO03NSnY5iymGlbwB4+btN5BQUceeQeKejGD9Ur1YYN5/ege837uWXzfudjmP+gJW+Yc/hPN5atIU/9YomvkV9p+MYP3X1KbFE1a/FU7NT8bXRe83/WOkbpnybRlGxcodt5ZsqqB0RyrgzOvLLlv38kLbX6TjmBKz0g1zmgRze+2UbFyfF0K5pXafjGD83pl8M0Y1q89ScDba176Os9IPcC/PTEITbzuzodBQTAGqFhXL7WR1ZmXGQeev2lL+AqXFW+kFs895sZizL5IqT29K6UW2n45gAcWGfNsQ1q8vTc1IpLratfV/jUemLyAgRSRWRNBGZUMbr40VkrYisEpH5ItLO7bVrRGSj6+sab4Y3VfPs3A1EhIZwy2DbyjfeExYawp1D4lm/6whfrN7pdBxTSrmlLyKhwBRgJJAIXCYiiaVmWw4kqWoPYAYw2bVsE2Ai0B/oB0wUkcbei28qa+2Ow8xcuYPrTy0548IYbzqvR2s6t6zPM3NSKSgqdjqOcePJln4/IE1V01U1H5gOjHafQVW/VdXjN8z8GWjjejwcmKuq+1X1ADAXGOGd6KYqnp6TSoPIMMYO6uB0FBOAQkKEvw3rxJZ9OcxYmul0HOPGk9KPBjLcnme6pp3IDcCsiiwrImNFJFlEkrOysjyIZKpi6db9zF+/h5tO70DDOuFOxzEB6qwuzendthHPz9tIXkGR03GMiyelX9Ztk8o8OiMiVwJJwJMVWVZVp6lqkqomRUXZDbirk6oy+etUmtWL4LqBsU7HMQFMRLh7eCd2Hc7jnZ+3Oh3HuHhS+plAjNvzNsCO0jOJyBDgfmCUqh6ryLKm5ny/cS+LN+9n3BkdqRMR5nQcE+AGdGjGqR2b8dKCTRzJK3A6jsGz0l8CxItInIhEAGOAme4ziEhvYColhe9+cu5sYJiINHYdwB3mmmYcUFysTJ69njaNa3NZ/7ZOxzFB4u7hndifnc+r3292OorBg9JX1UJgHCVlvQ74QFVTRGSSiIxyzfYkUA/4UERWiMhM17L7gUco+YdjCTDJNc044Ks1O1mz/TDjhyZQKyzU6TgmSPSMacTZ3Vvy6vfp7D16rPwFTLUSX7tUOikpSZOTk52OEXAKiooZ+sx31AoL5as7BhEaUtbhFmOqx6asowx7diFXndyOh0Z1dTpOQBKRpaqaVN58dkVukPggOYMt+3K4Z0QnK3xT4zpE1eOSpDa8u3grGftzyl/AVBsr/SCQm1/E8/M2ktSuMWd2bu50HBOk7jgrgRARu62iw6z0g8DrP25mz5Fj3DuyMyK2lW+c0bJhJNcOjOWTFdtZt/Ow03GClpV+gNufnc/LCzYxpEsL+sY2cTqOCXK3nN6RBpHh/HPWeqejBC0r/QD3wjcbyc4v5N4RnZyOYgwN64Rz6xkd+G5DFovsRiuOsNIPYNv25fDOz1u5tG+M3QbR+IyrT4klulFtHp+13oZedoCVfgB7ck4qoSHCnUMSnI5izK8iw0O5a1gCq7cf4vNVdoF+TbPSD1CrMg/y+cod/HlQe1o0iHQ6jjG/cX6vaLq0asBTc1I5VmiDsdUkK/0ApKo8+uU6mtaNYOxp7Z2OY8zvhIQI953dmYz9ubz9kw3GVpOs9APQ3LW7Wbx5P3cOTaB+pA2dbHzToPgoTk+I4l/zN3IgO9/pOEHDSj/AFBQV889Z6+kQVZfL+saUv4AxDrrv7C4cPVbIC9+kOR0laFjpB5j3Fm8jfW82953dhbBQ+99rfFunlvW5tG8Mb/+8hS17s52OExSsFQLIodwCnpu3gQEdmtpwC8Zv/HVoAhGhIXbBVg2x0g8gU75N42BuAfef08WGWzB+o3n9SG4+vQNfp+xicfo+p+MEPCv9ALFlbzZv/LiZi/q0oWvrhk7HMaZCbhzUntYNI5n0xVqK7IKtamWlHyAe/WodEaEh3G3DLRg/VDsilHtHdiZlx2E+WprpdJyAZqUfAH4xr1l4AAASfElEQVRM28vctbu59cyONK9vF2IZ/zSqZ2v6tG3E5Nmpdj/dauRR6YvICBFJFZE0EZlQxuunicgyESkUkYtKvVbkuoXir7dRNN5TWFTMpM/XEtOkNtcPjHM6jjGVJiJMPK8re48eY8q3m5yOE7DKLX0RCQWmACOBROAyEUksNds24FrgvTJWkauqvVxfo8p43VTB+0sySN19hPtGdiEy3O57a/xbz5hGXNAnmtd/2MzWfXYKZ3XwZEu/H5Cmqumqmg9MB0a7z6CqW1R1FVBcDRnNCRzIzufpOamc3L4JI7q1dDqOMV5x74jOhIcKj3yxzukoAcmT0o8GMtyeZ7qmeSpSRJJF5GcROb+sGURkrGue5KysrAqsOrg9NSeVI3mFPDyqm52iaQJGiwaR3HZWPPPW7ebb1D1Oxwk4npR+WW1SkXOq2rru0H458JyIdPjdylSnqWqSqiZFRUVVYNXBa832Q7z3yzauPqUdnVraWPkmsFw/MI72zeoy6fO1Ngqnl3lS+pmA+yAubQCPB8FW1R2u/6YDC4DeFchnylBcrDz42Rqa1ImwsfJNQIoIC2HiqK5s3pvNaz9sdjpOQPGk9JcA8SISJyIRwBjAo7NwRKSxiNRyPW4GDATWVjasKfHJ8u0s23aQe0d2pmFtG0XTBKbTE6IYltiCF+ansfNQrtNxAka5pa+qhcA4YDawDvhAVVNEZJKIjAIQkb4ikglcDEwVkRTX4l2AZBFZCXwL/FNVrfSr4FBOAY/PWkevmEZc1KeN03GMqVb/d24ixao88oXVhreEeTKTqn4FfFVq2oNuj5dQstun9HKLgO5VzGjcPDUnlf3Z+bx5XT9CQuzgrQlsMU3qcNuZHXlqzgYWpO5hcCcbSLCq7IpcP7Iy4yDvLN7K1afE0i3axtcxweHPp7WnfVRdJs5MIa/ADupWlZW+nygqVh74dA1R9Wpx1zA7eGuCR62wUP4xuhtb9+Xw0gK7UreqrPT9xLuLt7J6+yH+79xEuwWiCToDOjZjdK/WvLxgE+lZR52O49es9P3ArkN5TP46lVM7NuPcHq2cjmOMI+4/pwu1wkN44NM1qNrwy5Vlpe8HHvxsDYXFxTz6J7vy1gSv5vUj+fvILizatI8PbfjlSrPS93Ffr9nJnLW7uXNIAu2a1nU6jjGOGtM3hn6xTXj0y3VkHTnmdBy/ZKXvww7lFvDgZykktmrAjafasMnGhIQIj13Qndz8IibZufuVYqXvw574ej17jx7jiQt7EBZq/6uMAejYvB63ntGRz1fu4Jv1u52O43esSXzUorS9vLd4G9cPjKN7Gzsn3xh3fxncgYQW9bjv4zUctrtsVYiVvg/KPlbIvR+vIq5ZXe4aZve8Naa0iLAQnryoJ3uO5PHYlzbufkVY6fugyV+vJ/NALpMv6kHtCLsbljFl6RnTiJtO78D0JRks3GD34fCUlb6P+Tl9H2/9tJVrB8TSN7aJ03GM8Wl3nBVPx+b1mPDRKruZuoes9H1I9rFC7pmxirZN6nD3cNutY0x5IsNDmXxRD3YdzuNR283jESt9H/KPL9eRcSCHpy7uSZ0IjwZANSbo9WnbmLGnlezmmb/OzuYpj5W+j5i/bjfv/7KNsae1p1+c7dYxpiL+OjSeLq0acO9Hq9h31C7a+iNW+j5g39Fj3PvRajq3rM/4oTaCpjEVVSsslOcu7cXh3ELu+2S1jc3zB6z0Haaq3P/JGg7nFvDspb2oFWZn6xhTGZ1a1udvwxOYnbKbGTY2zwlZ6Tts+pIMvk7Zxd+GJ9ClVQOn4xjj1244tT3945rw0MwUNu/NdjqOT/Ko9EVkhIikikiaiEwo4/XTRGSZiBSKyEWlXrtGRDa6vq7xVvBAsHH3ER7+PIVB8c248dT2Tscxxu+FhgjPjelFeFgIt7+/nPzCYqcj+ZxyS19EQoEpwEggEbhMRBJLzbYNuBZ4r9SyTYCJQH+gHzBRRBpXPbb/yyso4rb3l1M3IoynL+lp97s1xktaNazNExf2YPX2Qzw1J9XpOD7Hky39fkCaqqaraj4wHRjtPoOqblHVVUDpf1aHA3NVdb+qHgDmAiO8kNvvPf7VOtbvOsJTF/ekef1Ip+MYE1CGd23JVSe3Y9rCdBak7nE6jk/xpPSjgQy355muaZ7waFkRGSsiySKSnJUV+JdTz1q9k7d+2sr1A+M4o3Nzp+MYE5DuP6cLnVrU564PVrLrUJ7TcXyGJ6Vf1n4HT8+H8mhZVZ2mqkmqmhQVFeXhqv3T5r3Z3D1jFb1iGjFhZGen4xgTsCLDQ5lyRR/yCooY994yCops/z54VvqZQIzb8zbADg/XX5VlA05eQRF/eWcpYaHClCv6EBFmJ08ZU506Nq/H4xf2IHnrASZ/vd7pOD7Bk9ZZAsSLSJyIRABjgJkern82MExEGrsO4A5zTQtKD362hvW7jvDspb2IblTb6TjGBIVRPVtz9SnteOX7zXy9ZpfTcRxXbumraiEwjpKyXgd8oKopIjJJREYBiEhfEckELgamikiKa9n9wCOU/MOxBJjkmhZ03l28lQ+SMxl3RkfO6GT78Y2pSfef04WebRpy94crSdtz1Ok4jhJfu1w5KSlJk5OTnY7hVclb9nPZKz8zoEMzXr+2L6F2eqYxNW77wVxGvfADDeuE8+mtA2kQGe50JK8SkaWqmlTefLZTuZrtOpTHze8sI7pRbf41prcVvjEOiW5Um5eu6MO2fTncOX0FxcW+tcFbU6z0q1FeQRE3vbOU3PxCpl2dRMM6gbVlYYy/6d++KRPPS+Sb9Xt4Zu4Gp+M4wgZtryaqyt0zVrEy4yBTrzqJhBb1nY5kjAGuPLkda7Yf5sVv0+jYvB7n9/b0sqPAYFv61eTZeRv5fOUO7h3RmeFdWzodxxjjIiI8cn43+sc14Z4Zq1iyJbjOLbHSrwYfL8vkX/M3cklSG24+3QZSM8bXRISFMPWqk4huXJux/0lm677gGZHTSt/Lftq0j3s/WsUp7Zvyj/O7I2IHbo3xRY3qRPD6tX1R4Lo3l3AgO9/pSDXCSt+L1u44zNj/JNOuaV3+faVdcWuMr4trVpdpVyWReSCX695cQk5+odORqp21kpdk7M/hmjd+oV5kGP+5vh+N6kQ4HckY44F+cU3415herMo8yK3vBv4YPVb6XrDv6DGufv0XjhUU8db1/WhtQywY41dGdGvFI+d349vULCZ8tDqgz+G3Uzar6FBOAVe+9gs7Duby7o397dRMY/zUFf3bkXXkGM/N20j9yDAmnpcYkMfkrPSr4EheAVe/8Qub9hzllWuSSIpt4nQkY0wV3HFWPEfzCnn1h83UCg9hwojOAVf8VvqVlJNfyA1vJpOy/RD/vvIkTk8I7PsAGBMMRIT7z+lCXmERU79Lp3Z4KHcOSXA6lldZ6VdC9rFCrn9zCclb9/P8mN4MTWzhdCRjjJeICJNGdSOvoJjn5m1EEG4/q2PAbPFb6VfQkbwCrntjCcszDvLspb04r2drpyMZY7wsJER44sIeADw7bwMFRcXcNSwhIIrfSr8CDuUWcPXrv5Cy/RAvXtabkd1bOR3JGFNNQkOEyRf2IDxUePHbNPKLivn7SP/fx2+l76E9h/O4+vVf2JR1lH9feZLt0jEmCISECI+e353w0BCmLUznSF4Bj4zuRlio/57tbqXvgc17s7nqtcUcyM7njWv7cWp8M6cjGWNqSEiI8PCorjSIDOfFb9PYdzSff13Wm8jwUKejVYpH/1yJyAgRSRWRNBGZUMbrtUTkv67XF4tIrGt6rIjkisgK19fL3o1f/VZlHuSify8iJ7+I98eebIVvTBASEf42vBMTz0tkztrdXPP6LxzKLXA6VqWUW/oiEgpMAUYCicBlIpJYarYbgAOq2hF4FnjC7bVNqtrL9XWzl3LXiK/X7OKSqT8RGR7KjJtPoUebRk5HMsY46LqBcTw/phfLth3ggpd+ZNu+HKcjVZgnW/r9gDRVTVfVfGA6MLrUPKOBt1yPZwBniR8f7VBVpn63ib+8u5TOLRvw6a0DaR9Vz+lYxhgfMLpXNG/f0J+9R/M5/6UfSfaz8fg9Kf1oIMPteaZrWpnzqGohcAho6notTkSWi8h3IjKoinmrXV5BEffMWMXjs9ZzdvdWTB97MlH1azkdyxjjQ05u35RPbhlAw9rhXP7KYj5Izih/IR/hSemXtcVeejSiE82zE2irqr2B8cB7ItLgd28gMlZEkkUkOSsry4NI1WP7wVwufvknPlyaye1nxfPCGP89WGOMqV7to+rxyS0D6BvXmHtmrOL+T1aTX+j7I3R6UvqZQIzb8zbAjhPNIyJhQENgv6oeU9V9AKq6FNgE/O6aZlWdpqpJqpoUFeXMcAY/bNzLeS/8wJa92bx6dRLjhyYQEuK3e6iMMTWgUZ0I3rquHzed3p53F2/j0mk/sfNQrtOx/pAnpb8EiBeROBGJAMYAM0vNMxO4xvX4IuAbVVURiXIdCEZE2gPxQLp3ontHQVExT85ez1WvL6Zp3Qg+GzeQIXYOvjHGQ2GhIfx9ZBemXN6H1F1HGPn898xdu9vpWCdU7nn6qlooIuOA2UAo8LqqpojIJCBZVWcCrwFvi0gasJ+SfxgATgMmiUghUATcrKo+c9Qj80AOt7+/nGXbDnJpUgwTRyVSJ8IuXTDGVNw5PVrRpVV9bnt/OX/+TzLXDohlwsjOPreLWFR962YBSUlJmpycXK3voap8mJzJI1+sBeCxC7rbGDrGGK84VljEP2et540ft5DQoh5PX9yL7m0aVvv7ishSVU0qbz7/vZa4kvYczuOGt5K556NVJLZuwFd3DLLCN8Z4Ta2wUCae15U3ruvLwZwCzn/pR56du8FnbsMYNFv6xcXK+0u28cSs9RwrLObeEZ25dkCsHaw1xlSbgzn5PDQzhU9X7KBzy/o8+qfunNSucbW8l6db+kFR+ut3Hea+j1ezbNtBTmnflEf/1M0utjLG1Jg5KbuYODOFXYfzuLxfW+4Z0ZmGtcO9+h6eln5AH7U8kJ3Ps/M28O7ibTSIDOPpi3tyQZ9ovx8a1RjjX4Z1bcmAjs14Zs4G3ly0mVlrdjF+aAJj+sbU+IidAbmlf6ywiHd/3sbz8zdyJK+AK/q3Y/zQBBrXjfBSSmOMqZw12w8x6fO1/LJlP51b1uf+c7owKL7q1ycF5e6domLlk+XbeXbuBrYfzOXUjs34v3MT6dSyvpdTGmNM5akqs9bs4rGv1pF5IJcBHZpy9/BO9G5b+f39QVf6GftzuO7NJaTtOUr36IbcPbwTg+Kb2a4cY4zPOr5XYsq3aezLzuecHq148bLeleqtoNun37JhJG2b1GH80ARGdmtpZW+M8Xm1wkK5/tQ4Lu0bw+s/bCavsKjauytgtvSNMSaY2cVZxhhjfsdK3xhjgoiVvjHGBBErfWOMCSJW+sYYE0Ss9I0xJohY6RtjTBCx0jfGmCDicxdniUgWsNXpHKU0A/Y6HcJh9hmUsM/BPoPjfO1zaKeq5Y7c5nOl74tEJNmTK90CmX0GJexzsM/gOH/9HGz3jjHGBBErfWOMCSJW+p6Z5nQAH2CfQQn7HOwzOM4vPwfbp2+MMUHEtvSNMSaIWOkbY0wQsdL3kIg8KSLrRWSViHwiIo2czlTTRORiEUkRkWIR8btT1apCREaISKqIpInIBKfzOEFEXheRPSKyxuksThGRGBH5VkTWuX4X7nA6U0VZ6XtuLtBNVXsAG4C/O5zHCWuAC4CFTgepSSISCkwBRgKJwGUikuhsKke8CYxwOoTDCoG7VLULcDJwq7/9LFjpe0hV56hqoevpz0AbJ/M4QVXXqWqq0zkc0A9IU9V0Vc0HpgOjHc5U41R1IbDf6RxOUtWdqrrM9fgIsA6IdjZVxVjpV871wCynQ5gaEw1kuD3PxM9+0Y33iUgs0BtY7GySiglzOoAvEZF5QMsyXrpfVT9zzXM/JX/ivVuT2WqKJ59BEJIyptm5zkFMROoBHwF3quphp/NUhJW+G1Ud8kevi8g1wLnAWRqgFziU9xkEqUwgxu15G2CHQ1mMw0QknJLCf1dVP3Y6T0XZ7h0PicgI4F5glKrmOJ3H1KglQLyIxIlIBDAGmOlwJuMAERHgNWCdqj7jdJ7KsNL33ItAfWCuiKwQkZedDlTTRORPIpIJnAJ8KSKznc5UE1wH8McBsyk5cPeBqqY4m6rmicj7wE9AJxHJFJEbnM7kgIHAVcCZrh5YISJnOx2qImwYBmOMCSK2pW+MMUHESt8YY4KIlb4xxgQRK31jjAkiVvrGGBNErPSNMSaIWOkbY0wQ+X85JMJYOSalywAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6b97fa4e48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, frozen_norm.pdf(x))\n",
    "plt.title(\"Normal Distribution\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array(0.), array(1.), array(0.), array(0.))"
      ]
     },
     "execution_count": 108,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean, var, skew, kurt = stats.norm.stats(moments='mvsk')\n",
    "mean, var, skew, kurt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-2.80828356,  0.34944895, -0.30748255, -1.32152462, -2.12881871,\n",
       "       -0.26429612,  0.9235659 ,  0.7102103 ,  1.01960184, -0.29352855])"
      ]
     },
     "execution_count": 109,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Random variates\n",
    "# scipy.stats.norm.rvs(loc=0, scale=1, size=1, random_state=None)\n",
    "stats.norm.rvs(size=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f6b97b41be0>"
      ]
     },
     "execution_count": 110,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6b97c08cc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(1, 3, figsize=(20, 5))\n",
    "x = np.linspace(stats.norm.ppf(0.01), stats.norm.ppf(0.99), 100)\n",
    "axes[0].plot(x, stats.norm.pdf(x), 'r-', lw=5, alpha=0.5, label='norm pdf')\n",
    "axes[0].legend(loc='best', frameon=True)\n",
    "\n",
    "rv = stats.norm()\n",
    "axes[1].plot(x, rv.pdf(x), 'g-', lw=5, label='frozen pdf')\n",
    "axes[1].legend(loc='best', frameon=True)\n",
    "\n",
    "r = stats.norm.rvs(size=1000)\n",
    "axes[2].hist(r, normed=True, histtype='stepfilled', alpha=0.7, label='histogram')\n",
    "axes[2].legend(loc='best', frameon=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [],
   "source": [
    "vals = stats.norm.ppf([0.001, 0.5, 0.999])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-3.09023231,  0.        ,  3.09023231])"
      ]
     },
     "execution_count": 112,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.001, 0.5  , 0.999])"
      ]
     },
     "execution_count": 113,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.norm.cdf(vals)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 114,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"\"\"\n",
    "Returns True if two arrays are element-wise equal within a tolerance.\n",
    "\"\"\"\n",
    "np.allclose([0.001, 0.5, 0.999], stats.norm.cdf(vals))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [],
   "source": [
    "my_data = np.random.uniform(-3, 3, (3, 5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.9673439933883938"
      ]
     },
     "execution_count": 116,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "my_data.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0721042952052813"
      ]
     },
     "execution_count": 117,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "my_data.var()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Numpy is restricted to fairly basic array operations, you need to reach out to it's more educated brother, Scipy, to get more advanced stats functions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [],
   "source": [
    "import scipy as sp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.9673439933883938"
      ]
     },
     "execution_count": 119,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sp.mean(my_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0721042952052813"
      ]
     },
     "execution_count": 120,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sp.var(my_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.035424693159904"
      ]
     },
     "execution_count": 121,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sp.std(my_data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Skew & Kurtosis\n",
    "\n",
    "A fundamental task in many statistical analyses is to characterize the location and variability of a data set. \n",
    "A further characterization of the data includes skewness and kurtosis. Skewness is a measure of symmetry, or \n",
    "more precisely, the lack of symmetry. A distribution, or data set, is symmetric if it looks the same to the \n",
    "left and right of the center point.\n",
    "\n",
    "Kurtosis is a measure of whether the data are heavy-tailed or light-tailed relative to a normal distribution.\n",
    "That is, data sets with high kurtosis tend to have heavy tails, or outliers. Data sets with low kurtosis tend \n",
    "to have light tails, or lack of outliers. A uniform distribution would be the extreme case.\n",
    "\n",
    "The histogram is an effective graphical technique for showing both the skewness and kurtosis of data set."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<dl class=\"function\">\n",
    "<dt id=\"scipy.stats.kurtosis\">\n",
    "<!--[scipy.stats.kurtosis]--><tt class=\"descclassname\">scipy.stats.</tt><tt class=\"descname\">kurtosis</tt><big>(</big><em>a</em>, <em>axis=0</em>, <em>fisher=True</em>, <em>bias=True</em><big>)</big><a class=\"headerlink\" href=\"#scipy.stats.kurtosis\" title=\"Permalink to this definition\">¶</a></dt>\n",
    "<dd><p>Computes the kurtosis (Fisher or Pearson) of a dataset.</p>\n",
    "<p>Kurtosis is the fourth central moment divided by the square of the variance.\n",
    "If Fisher’s definition is used, then 3.0 is subtracted from the result to\n",
    "give 0.0 for a normal distribution.</p>\n",
    "<p>If bias is False then the kurtosis is calculated using k statistics to\n",
    "eliminate bias comming from biased moment estimators</p>\n",
    "<p>Use kurtosistest() to see if result is close enough to normal.</p>\n",
    "<table class=\"docutils field-list\" frame=\"void\" rules=\"none\">\n",
    "<colgroup><col class=\"field-name\">\n",
    "<col class=\"field-body\">\n",
    "</colgroup><tbody valign=\"top\">\n",
    "<tr class=\"field\"><th class=\"field-name\">Parameters:</th><td class=\"field-body\"><p class=\"first\"><strong>a</strong> : array</p>\n",
    "<p><strong>axis</strong> : int or None</p>\n",
    "<p><strong>fisher</strong> : bool</p>\n",
    "<blockquote>\n",
    "<p>If True, Fisher’s definition is used (normal ==&gt; 0.0). If False,\n",
    "Pearson’s definition is used (normal ==&gt; 3.0).</p>\n",
    "</blockquote>\n",
    "<p><strong>bias</strong> : bool</p>\n",
    "<blockquote>\n",
    "<p>If False, then the calculations are corrected for statistical bias.</p>\n",
    "</blockquote>\n",
    "</td>\n",
    "</tr>\n",
    "<tr class=\"field\"><th class=\"field-name\">Returns:</th><td class=\"field-body\"><p class=\"first\"><strong>The kurtosis of values along an axis. If all values are equal, return -3 for Fisher’s</strong> :</p>\n",
    "<p class=\"last\"><strong>definition and 0 for Pearson’s definition.</strong> :</p>\n",
    "</td>\n",
    "</tr>\n",
    "</tbody>\n",
    "</table>\n",
    "<p class=\"rubric\">References</p>\n",
    "<p>[CRCProbStat2000] section 2.2.25</p>\n",
    "</dd></dl>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In statistics, the bias (or bias function) of an estimator is the difference between this estimator's expected value and the true value of the parameter being estimated. An estimator or decision rule with zero bias is called unbiased. Otherwise the estimator is said to be biased."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.66452636, 4.61807115, 4.1339752 ])"
      ]
     },
     "execution_count": 122,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sp.stats.kurtosis(my_data, axis=1, fisher=False, bias=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A symmetrical dataset will have a skewness equal to 0. So, a normal distribution will have \n",
    "a skewness of 0. ... The value is often compared to the kurtosis of the normal distribution,\n",
    "which is equal to 3. If the kurtosis is greater than 3, then the dataset has heavier tails than\n",
    "a normal distribution (more in the tails).\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.66582843, -0.37462782,  0.08368999,  0.4245724 ,  0.30483592])"
      ]
     },
     "execution_count": 123,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sp.stats.skew(my_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DescribeResult(nobs=3, minmax=(array([-2.86072336, -0.73948857, -2.03890582, -0.86232183, -1.59043236]), array([ 1.10665294, -0.38721087, -1.47450926,  0.43451477,  0.00818815])), mean=array([-1.37364067, -0.54420052, -1.76315378, -0.29553077, -0.86019422]), variance=array([4.67486962, 0.03212497, 0.07976053, 0.44043531, 0.65320975]), skewness=array([ 0.66582843, -0.37462782,  0.08368999,  0.4245724 ,  0.30483592]), kurtosis=array([-1.5, -1.5, -1.5, -1.5, -1.5]))"
      ]
     },
     "execution_count": 124,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sp.stats.describe(my_data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Kurtosis is helpful to find outliers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Probability distributions</h3>\n",
    "\n",
    "<p>\n",
    "Scipy has functions that deal with several common probability distributions. Currently there are 81 continuous probability distributions and 10 discrete distributions. These are defined in the scipy.stats sub-package. This package also defines several statistical functions.\n",
    "</p>\n",
    "\n",
    "<h4>\n",
    "Examples of continuous probability distributions are:\n",
    "</h4>\n",
    "\n",
    "<table>\n",
    "    <tr>\n",
    "        <td>norm :</td><td> Normal or Gaussian</td>\n",
    "    </tr><tr><td>chi2 :</td><td> Chi-squared</td>\n",
    "    </tr><tr><td>uniform :</td><td> Uniform</td>\n",
    "    </tr>\n",
    "</table>\n",
    "    \n",
    "<h4>Examples of discrete probability distributions are:</h4>\n",
    "\n",
    "<table><tr>\n",
    "    <td>binom :</td><td> Binomial</td>\n",
    "    </tr><tr><td>poisson :</td><td> Poisson</td>\n",
    "    </tr></table>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### There are two ways of using probability distribution functions.\n",
    "\n",
    "1 - Generate a “frozen” distribution object and then work with the methods of this object. A “frozen” distribution is one with its parameters set to specific values. For example a Gaussian with mean = 3.5 and standard deviation = 2.0."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [],
   "source": [
    " n = sp.stats.norm(loc=3.5, scale=2.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.632776013190175"
      ]
     },
     "execution_count": 132,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n.rvs()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2 - Use functions in the appropriate class by always passing the parameters that define the distribution, when calling functions associated with the distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.392965245461745"
      ]
     },
     "execution_count": 133,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sp.stats.norm.rvs(3.5, 2.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### CDF, PDF, PMF, PPF"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.00897006, 0.22980519, 0.03786265, 0.32319419, 0.15905764],\n",
       "       [0.86577799, 0.34930005, 0.02072971, 0.66804266, 0.50326656],\n",
       "       [0.00211338, 0.30646268, 0.07017226, 0.19425522, 0.05586869]])"
      ]
     },
     "execution_count": 145,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sp.stats.norm.cdf(my_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 156,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f6b9756e898>]"
      ]
     },
     "execution_count": 156,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6b978cbcf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(sp.stats.norm.cdf(np.linspace(-3, 3, 50)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 157,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f6b974d1668>]"
      ]
     },
     "execution_count": 157,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6b97a5b048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(sp.stats.norm.pdf(np.linspace(-3, 3, 50)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "PPF is the inverse of the CDF. That is, PPF gives the value of the variate for which \n",
    "the cumulative probability has the given value."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 160,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 160,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sp.stats.norm.ppf(0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 174,
   "metadata": {},
   "outputs": [],
   "source": [
    "n = 5.0\n",
    "p = 0.4\n",
    "lw = sp.stats.binom.ppf(0.01, n, p)\n",
    "up = sp.stats.binom.ppf(0.99, n, p)\n",
    "x = np.arange(lw, up)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 175,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6b97326ac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rv = sp.stats.binom(n, p)\n",
    "plt.vlines(x, 0, rv.pmf(x), colors='k', linestyles='-', lw=1, label='frozen pmf')\n",
    "plt.legend(loc='best', frameon=False)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 195,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'boxes': [<matplotlib.lines.Line2D at 0x7f6b96cfa240>],\n",
       " 'caps': [<matplotlib.lines.Line2D at 0x7f6b96cfac50>,\n",
       "  <matplotlib.lines.Line2D at 0x7f6b96d070b8>],\n",
       " 'fliers': [<matplotlib.lines.Line2D at 0x7f6b96d07908>],\n",
       " 'means': [],\n",
       " 'medians': [<matplotlib.lines.Line2D at 0x7f6b96d074e0>],\n",
       " 'whiskers': [<matplotlib.lines.Line2D at 0x7f6b96cfa390>,\n",
       "  <matplotlib.lines.Line2D at 0x7f6b96cfa828>]}"
      ]
     },
     "execution_count": 195,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6b970916a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.boxplot(np.random.normal(0, 5, 10), vert=0)"
   ]
  }
 ],
 "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": "3.6.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}