{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# IntroStat Week 7\n",
    "\n",
    "Welcome to the 7th lecture in IntroStat\n",
    "\n",
    "During the lectures we will present both slides and notebooks. \n",
    "\n",
    "This is the notebook used in the lecture in week 7.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.stats as stats\n",
    "import statsmodels.api as sm\n",
    "import statsmodels.stats.power as smp"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example: Area of plates"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Simulating from 2 normal distributions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6.000036032465656\n",
      "0.05010905153998061\n"
     ]
    }
   ],
   "source": [
    "k = 100000\n",
    "X = stats.norm.rvs(size=k, loc=2, scale=0.01) # length\n",
    "Y = stats.norm.rvs(size=k, loc=3, scale=0.02) # width\n",
    "A = X*Y # area\n",
    "\n",
    "# Compute mean and standard deviation from simulated data:\n",
    "print(A.mean())      # mean area\n",
    "print(A.std(ddof=1)) # sample standard deviation of area"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Lets plot the distribution of simulated areas:\n",
    "plt.hist(A, bins=100)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.04544\n"
     ]
    }
   ],
   "source": [
    "# how many values deviate bu more than 0.10 from 6m2 ?\n",
    "print((np.sum(A > 6.10) + np.sum(A < 5.90)) / k)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.002510917046236433"
      ]
     },
     "execution_count": 124,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# variance of area\n",
    "A.var(ddof=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the simulated data we could also compute other statistics - median of area, IQR of area, etc"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example: CI for exponential rate or mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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e6dXHuxl+vyHf9hQAALiuG/353aNrRtra2iRJo0aN6nJMTU2NcnNzo/bl5eWppqamy2NCoZCCwWDUBgAAnGlQdw8Mh8NatWqV7rzzTk2dOrXLcYFAQElJSVH7kpKSFAgEujzG7/dr3bp13Z0a0Gs4cwYAfa/bZ0aKi4vV0NCgioqK3pyPJKm0tFRtbW2RrampqdefAwAAfDF068zIypUrtXfvXh0+fFhjx4695liv16uWlpaofS0tLfJ6vV0e43a75Xa7uzM1AADQz8R0ZsQYo5UrV2r37t06cOCAMjIyrnuMz+dTdXV11L6qqir5fL7YZgoAABwppjMjxcXFKi8v1549ezR8+PDIdR8ej0dDhgyRJBUWFio1NVV+v1+SVFJSonnz5mnTpk3Kz89XRUWFamtrtX379l5eCgAA6I9iOjOydetWtbW1af78+UpOTo5sL7zwQmRMY2OjmpubI7dzcnJUXl6u7du3KysrSy+99JIqKyuvedErAAC4dcR0ZuRGPpLk4MGDV+279957de+998byVAAA4BbB36YBAABWESMAAMAqYgQAAFhFjAAAAKuIEQAAYBUxAgAArCJGAACAVcQIAACwihgBAABWESMAAMAqYgQAAFhFjAAAAKuIEQAAYBUxAgAArCJGAACAVcQIAACwihgBAABWESMAAMAqYgQAAFhFjAAAAKuIEQAAYBUxAgAArCJGAACAVcQIAACwihgBAABWESMAAMAqYgQAAFhFjAAAAKuIEQAAYBUxAgAArCJGAACAVcQIAACwihgBAABWxRwjhw8f1j333KOUlBS5XC5VVlZec/zBgwflcrmu2gKBQHfnDAAAHCTmGGlvb1dWVpa2bNkS03GnT59Wc3NzZEtMTIz1qQEAgAMNivWABQsWaMGCBTE/UWJiokaMGBHzcQAAwNlu2jUj06dPV3Jysu6++2796le/uubYUCikYDAYtQEAAGfq8xhJTk7Wtm3b9LOf/Uw/+9nPlJaWpvnz5+vEiRNdHuP3++XxeCJbWlpaX08TAABYEvOvaWI1ceJETZw4MXI7JydHv/vd7/Tkk0/qv/7rvzo9prS0VKtXr47cDgaDBAkAAA7V5zHSmdmzZ+vIkSNd3u92u+V2u2/ijAAAgC1WPmekvr5eycnJNp4aAAB8wcR8ZuTixYs6c+ZM5PbZs2dVX1+vUaNGKT09XaWlpfrggw/0n//5n5Kkp556ShkZGbr99tv12Wef6dlnn9WBAwf0i1/8ovdWAQAA+q2YY6S2tlZf//rXI7evXNtRVFSksrIyNTc3q7GxMXL/pUuX9J3vfEcffPCBhg4dqszMTP3yl7+MegwAAHDrijlG5s+fL2NMl/eXlZVF3X744Yf18MMPxzwxAABwa+Bv0wAAAKuIEQAAYBUxAgAArCJGAACAVcQIAACwihgBAABWESMAAMAqYgQAAFhFjAAAAKuIEQAAYBUxAgAArCJGAACAVcQIAACwihgBAABWESMAAMAqYgQAAFhFjAAAAKuIEQAAYBUxAgAArCJGAACAVcQIAACwihgBAABWESMAAMAqYgQAAFhFjAAAAKuIEQAAYBUxAgAArCJGAACAVcQIAACwihgBAABWESMAAMAqYgQAAFhFjAAAAKtijpHDhw/rnnvuUUpKilwulyorK697zMGDBzVz5ky53W5NmDBBZWVl3ZgqAABwophjpL29XVlZWdqyZcsNjT979qzy8/P19a9/XfX19Vq1apWWLVum/fv3xzxZAADgPINiPWDBggVasGDBDY/ftm2bMjIytGnTJknS5MmTdeTIET355JPKy8uL9ekBAIDD9Pk1IzU1NcrNzY3al5eXp5qami6PCYVCCgaDURsAAHCmmM+MxCoQCCgpKSlqX1JSkoLBoD799FMNGTLkqmP8fr/WrVvX11Prt8avecX2FGL2+w35tqeAL7D++DXdH/Hf4c3RH7+ebX9tfCHfTVNaWqq2trbI1tTUZHtKAACgj/T5mRGv16uWlpaofS0tLUpISOj0rIgkud1uud3uvp4aAAD4AujzMyM+n0/V1dVR+6qqquTz+fr6qQEAQD8Qc4xcvHhR9fX1qq+vl/T5W3fr6+vV2Ngo6fNfsRQWFkbGr1ixQu+9954efvhhvf322/rRj36kF198Ud/+9rd7ZwUAAKBfizlGamtrNWPGDM2YMUOStHr1as2YMUOPPvqoJKm5uTkSJpKUkZGhV155RVVVVcrKytKmTZv07LPP8rZeAAAgqRvXjMyfP1/GmC7v7+zTVefPn6+6urpYnwoAANwCvpDvpgEAALcOYgQAAFhFjAAAAKuIEQAAYBUxAgAArCJGAACAVcQIAACwihgBAABWESMAAMAqYgQAAFhFjAAAAKuIEQAAYBUxAgAArCJGAACAVcQIAACwihgBAABWESMAAMAqYgQAAFhFjAAAAKuIEQAAYBUxAgAArCJGAACAVcQIAACwihgBAABWESMAAMAqYgQAAFhFjAAAAKuIEQAAYBUxAgAArCJGAACAVcQIAACwihgBAABWESMAAMCqbsXIli1bNH78eMXHx2vOnDl66623uhxbVlYml8sVtcXHx3d7wgAAwFlijpEXXnhBq1ev1tq1a3XixAllZWUpLy9Pra2tXR6TkJCg5ubmyHbu3LkeTRoAADhHzDHyxBNPaPny5br//vs1ZcoUbdu2TUOHDtWOHTu6PMblcsnr9Ua2pKSkHk0aAAA4R0wxcunSJR0/fly5ubl/eoABA5Sbm6uampouj7t48aLGjRuntLQ0LVy4UKdOnbrm84RCIQWDwagNAAA4U0wx8tFHH6mjo+OqMxtJSUkKBAKdHjNx4kTt2LFDe/bs0c6dOxUOh5WTk6P333+/y+fx+/3yeDyRLS0tLZZpAgCAfqTP303j8/lUWFio6dOna968eXr55Zf1pS99Sc8880yXx5SWlqqtrS2yNTU19fU0AQCAJYNiGTxmzBgNHDhQLS0tUftbWlrk9Xpv6DEGDx6sGTNm6MyZM12OcbvdcrvdsUwNAAD0UzGdGYmLi1N2draqq6sj+8LhsKqrq+Xz+W7oMTo6OnTy5EklJyfHNlMAAOBIMZ0ZkaTVq1erqKhIs2bN0uzZs/XUU0+pvb1d999/vySpsLBQqamp8vv9kqTHHntMc+fO1YQJE3T+/Hlt3LhR586d07Jly3p3JQAAoF+KOUYWLVqkDz/8UI8++qgCgYCmT5+u1157LXJRa2NjowYM+NMJl48//ljLly9XIBDQyJEjlZ2draNHj2rKlCm9twoAANBvxRwjkrRy5UqtXLmy0/sOHjwYdfvJJ5/Uk08+2Z2nAQAAtwD+Ng0AALCKGAEAAFYRIwAAwCpiBAAAWEWMAAAAq4gRAABgFTECAACsIkYAAIBVxAgAALCKGAEAAFYRIwAAwCpiBAAAWEWMAAAAq4gRAABgFTECAACsIkYAAIBVxAgAALCKGAEAAFYRIwAAwCpiBAAAWEWMAAAAq4gRAABgFTECAACsIkYAAIBVxAgAALCKGAEAAFYRIwAAwCpiBAAAWEWMAAAAq4gRAABgFTECAACsIkYAAIBVxAgAALCqWzGyZcsWjR8/XvHx8ZozZ47eeuuta47ftWuXJk2apPj4eE2bNk379u3r1mQBAIDzxBwjL7zwglavXq21a9fqxIkTysrKUl5enlpbWzsdf/ToUS1evFhLly5VXV2dCgoKVFBQoIaGhh5PHgAA9H8xx8gTTzyh5cuX6/7779eUKVO0bds2DR06VDt27Oh0/ObNm/XNb35TDz30kCZPnqz169dr5syZevrpp3s8eQAA0P8NimXwpUuXdPz4cZWWlkb2DRgwQLm5uaqpqen0mJqaGq1evTpqX15eniorK7t8nlAopFAoFLnd1tYmSQoGg7FM94aEQ5/0+mPian3x2t0M/fHroz/+W/fHf+f+qD9+bfRH/fHrua++Nq48rjHmmuNiipGPPvpIHR0dSkpKitqflJSkt99+u9NjAoFAp+MDgUCXz+P3+7Vu3bqr9qelpcUyXXyBeJ6yPYNbB//W6ApfG+hKX39tXLhwQR6Pp8v7Y4qRm6W0tDTqbEo4HNYf//hHjR49Wi6X64YeIxgMKi0tTU1NTUpISOirqVrHOp2FdToL63QW1hk7Y4wuXLiglJSUa46LKUbGjBmjgQMHqqWlJWp/S0uLvF5vp8d4vd6YxkuS2+2W2+2O2jdixIhYphqRkJDg6C+aK1ins7BOZ2GdzsI6Y3OtMyJXxHQBa1xcnLKzs1VdXR3ZFw6HVV1dLZ/P1+kxPp8varwkVVVVdTkeAADcWmL+Nc3q1atVVFSkWbNmafbs2XrqqafU3t6u+++/X5JUWFio1NRU+f1+SVJJSYnmzZunTZs2KT8/XxUVFaqtrdX27dt7dyUAAKBfijlGFi1apA8//FCPPvqoAoGApk+frtdeey1ykWpjY6MGDPjTCZecnByVl5fr+9//vh555BHddtttqqys1NSpU3tvFZ1wu91au3btVb/ucRrW6Sys01lYp7Owzr7jMtd7vw0AAEAf4m/TAAAAq4gRAABgFTECAACsIkYAAIBVjoyRLVu2aPz48YqPj9ecOXP01ltv2Z5Sjx0+fFj33HOPUlJS5HK5rvrbPsYYPfroo0pOTtaQIUOUm5urd999185ku8nv9+uOO+7Q8OHDlZiYqIKCAp0+fTpqzGeffabi4mKNHj1aw4YN09///d9f9aF6X3Rbt25VZmZm5AOFfD6fXn311cj9TlhjZzZs2CCXy6VVq1ZF9jlhrf/2b/8ml8sVtU2aNClyvxPWeMUHH3ygf/zHf9To0aM1ZMgQTZs2TbW1tZH7nfB9SJLGjx9/1WvqcrlUXFwsyRmvaUdHh37wgx8oIyNDQ4YM0Ve+8hWtX78+6m/I3NTX0zhMRUWFiYuLMzt27DCnTp0yy5cvNyNGjDAtLS22p9Yj+/btM9/73vfMyy+/bCSZ3bt3R92/YcMG4/F4TGVlpfn1r39tvvWtb5mMjAzz6aef2plwN+Tl5ZnnnnvONDQ0mPr6evM3f/M3Jj093Vy8eDEyZsWKFSYtLc1UV1eb2tpaM3fuXJOTk2Nx1rH7+c9/bl555RXzzjvvmNOnT5tHHnnEDB482DQ0NBhjnLHG/++tt94y48ePN5mZmaakpCSy3wlrXbt2rbn99ttNc3NzZPvwww8j9zthjcYY88c//tGMGzfO3HfffebNN9807733ntm/f785c+ZMZIwTvg8ZY0xra2vU61lVVWUkmddff90Y44zX9PHHHzejR482e/fuNWfPnjW7du0yw4YNM5s3b46MuZmvp+NiZPbs2aa4uDhyu6Ojw6SkpBi/329xVr3r/8dIOBw2Xq/XbNy4MbLv/Pnzxu12m//+7/+2MMPe0draaiSZQ4cOGWM+X9PgwYPNrl27ImP+93//10gyNTU1tqbZK0aOHGmeffZZR67xwoUL5rbbbjNVVVVm3rx5kRhxylrXrl1rsrKyOr3PKWs0xpjvfve75i//8i+7vN+p34eMMaakpMR85StfMeFw2DGvaX5+vnnggQei9v3d3/2dWbJkiTHm5r+ejvo1zaVLl3T8+HHl5uZG9g0YMEC5ubmqqamxOLO+dfbsWQUCgah1ezwezZkzp1+vu62tTZI0atQoSdLx48d1+fLlqHVOmjRJ6enp/XadHR0dqqioUHt7u3w+nyPXWFxcrPz8/Kg1Sc56Pd99912lpKToy1/+spYsWaLGxkZJzlrjz3/+c82aNUv33nuvEhMTNWPGDP34xz+O3O/U70OXLl3Szp079cADD8jlcjnmNc3JyVF1dbXeeecdSdKvf/1rHTlyRAsWLJB081/PL+Rf7e2ujz76SB0dHZFPg70iKSlJb7/9tqVZ9b1AICBJna77yn39TTgc1qpVq3TnnXdGPq03EAgoLi7uqj+a2B/XefLkSfl8Pn322WcaNmyYdu/erSlTpqi+vt4xa5SkiooKnThxQseOHbvqPqe8nnPmzFFZWZkmTpyo5uZmrVu3Tn/1V3+lhoYGx6xRkt577z1t3bpVq1ev1iOPPKJjx47pX//1XxUXF6eioiJHfh+SpMrKSp0/f1733XefJOd83a5Zs0bBYFCTJk3SwIED1dHRoccff1xLliyRdPN/rjgqRuAcxcXFamho0JEjR2xPpU9MnDhR9fX1amtr00svvaSioiIdOnTI9rR6VVNTk0pKSlRVVaX4+Hjb0+kzV/6fpCRlZmZqzpw5GjdunF588UUNGTLE4sx6Vzgc1qxZs/Tv//7vkqQZM2aooaFB27ZtU1FRkeXZ9Z2f/OQnWrBggVJSUmxPpVe9+OKLev7551VeXq7bb79d9fX1WrVqlVJSUqy8no76Nc2YMWM0cODAq65qbmlpkdfrtTSrvndlbU5Z98qVK7V37169/vrrGjt2bGS/1+vVpUuXdP78+ajx/XGdcXFxmjBhgrKzs+X3+5WVlaXNmzc7ao3Hjx9Xa2urZs6cqUGDBmnQoEE6dOiQ/uM//kODBg1SUlKSY9b650aMGKGvfvWrOnPmjKNez+TkZE2ZMiVq3+TJkyO/knLa9yFJOnfunH75y19q2bJlkX1OeU0feughrVmzRv/wD/+gadOm6Z/+6Z/07W9/O/JHbm/26+moGImLi1N2draqq6sj+8LhsKqrq+Xz+SzOrG9lZGTI6/VGrTsYDOrNN9/sV+s2xmjlypXavXu3Dhw4oIyMjKj7s7OzNXjw4Kh1nj59Wo2Njf1qnZ0Jh8MKhUKOWuNdd92lkydPqr6+PrLNmjVLS5Ysifxvp6z1z128eFG/+93vlJyc7KjX884777zqrfbvvPOOxo0bJ8k534f+3HPPPafExETl5+dH9jnlNf3kk0+i/qitJA0cOFDhcFiShdez1y+JtayiosK43W5TVlZmfvvb35p//ud/NiNGjDCBQMD21HrkwoULpq6uztTV1RlJ5oknnjB1dXXm3LlzxpjP34I1YsQIs2fPHvOb3/zGLFy4sN+9pe7BBx80Ho/HHDx4MOptdZ988klkzIoVK0x6ero5cOCAqa2tNT6fz/h8Pouzjt2aNWvMoUOHzNmzZ81vfvMbs2bNGuNyucwvfvELY4wz1tiVP383jTHOWOt3vvMdc/DgQXP27Fnzq1/9yuTm5poxY8aY1tZWY4wz1mjM52/PHjRokHn88cfNu+++a55//nkzdOhQs3PnzsgYJ3wfuqKjo8Okp6eb7373u1fd54TXtKioyKSmpkbe2vvyyy+bMWPGmIcffjgy5ma+no6LEWOM+eEPf2jS09NNXFycmT17tnnjjTdsT6nHXn/9dSPpqq2oqMgY8/nbsH7wgx+YpKQk43a7zV133WVOnz5td9Ix6mx9ksxzzz0XGfPpp5+af/mXfzEjR440Q4cONX/7t39rmpub7U26Gx544AEzbtw4ExcXZ770pS+Zu+66KxIixjhjjV35/zHihLUuWrTIJCcnm7i4OJOammoWLVoU9dkbTljjFf/zP/9jpk6datxut5k0aZLZvn171P1O+D50xf79+42kTufvhNc0GAyakpISk56ebuLj482Xv/xl873vfc+EQqHImJv5erqM+bOPWwMAALjJHHXNCAAA6H+IEQAAYBUxAgAArCJGAACAVcQIAACwihgBAABWESMAAMAqYgQAAFhFjAAAAKuIEQAAYBUxAgAArCJGAACAVf8HC+mRDEdhCd8AAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "wait_times = np.array([32.6, 1.6, 42.1, 29.2, 53.4, 79.3, 2.3, 4.7, 13.6, 2.0])\n",
    "\n",
    "plt.hist(wait_times)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We think the underlying distribution is an exponential distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "26.080000000000002\n"
     ]
    }
   ],
   "source": [
    "# lets compute the mean from data: \n",
    "print(wait_times.mean())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.03834355828220859\n"
     ]
    }
   ],
   "source": [
    "# calculate average rate:\n",
    "lamb = 1/wait_times.mean()\n",
    "print(lamb)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now make the assumption that the data comes from an underlying exponential distribution with same average rate as observed in sample:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# first we visualise the assumption of underlying distribution:\n",
    "x = np.arange(0,100,.1)\n",
    "plt.hist(wait_times, density=True)\n",
    "plt.plot(x, stats.expon.pdf(x, scale=1/lamb))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Simulation from exponential distribution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# run this cell several times to visualise simulations\n",
    "\n",
    "sim_wait_times = stats.expon.rvs(size=10, scale=1/lamb)\n",
    "\n",
    "plt.hist(wait_times,density=True, bins=10)\n",
    "plt.plot(x, stats.expon.pdf(x, scale=1/lamb))\n",
    "\n",
    "plt.hist(sim_wait_times,density=True, bins=10, alpha=0.3)\n",
    "\n",
    "plt.xlim(0,100)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Now do 100000 simulations\n",
    "k = 100000\n",
    "sim_wait_times = stats.expon.rvs(size=(k,10), scale=1/lamb)\n",
    "\n",
    "# for each simulation we calculate the mean:\n",
    "sim_means = sim_wait_times.mean(axis=1)\n",
    "\n",
    "# now we plot a histogram of all the (100000) mean values\n",
    "plt.hist(sim_means, density=True, bins=30)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For each simulation we had n = 10. \n",
    "\n",
    "This is not very large and CLT does not apply - we also see in the plot above that the distribution of the means does not look like a normal distribution\n",
    "\n",
    "(according to the CLT it should approach a normal distribution as n increases - try this yourself. How large do YOU think n should be? Do you agree that maybe n>30 is not always enough?)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[12.47768831 44.67685963]\n"
     ]
    }
   ],
   "source": [
    "# From simulated means we can find the 95% CI for the mean:\n",
    "CI = np.percentile(sim_means, [2.5, 97.5], method=\"averaged_inverted_cdf\")\n",
    "print(CI)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We just made a simulation based confidence interval for the mean :-)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 153,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# visualisation of the CI for the mean:\n",
    "plt.hist(sim_means, density=True, bins=30)\n",
    "plt.plot([wait_times.mean(), wait_times.mean()], [0,0.05], '-', color=\"black\")\n",
    "plt.plot([12.57, 12.57], [0,0.05], '--', color=\"black\")\n",
    "plt.plot([44.35, 44.35], [0,0.05], '--', color=\"black\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example: CI for median"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What about other statistics - like the median?\n",
    "\n",
    "We can use same approach!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 158,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 7.09823128 38.30277421]\n"
     ]
    }
   ],
   "source": [
    "# for each simulation we calculate the median:\n",
    "sim_medians = np.median(sim_wait_times, axis=1)\n",
    "\n",
    "# From simulated medians we can find the 0.025 and 0.975 fractiles:\n",
    "CI = np.percentile(sim_medians, [2.5, 97.5], method=\"averaged_inverted_cdf\")\n",
    "print(CI)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 159,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# we also visualise the CI for median (and histogram of simulated medians)\n",
    "plt.hist(sim_medians, density=True, bins=30)\n",
    "plt.plot([np.median(wait_times), np.median(wait_times)], [0,0.05], '-', color=\"black\")\n",
    "plt.plot([CI[0], CI[0]], [0,0.05], '--', color=\"black\")\n",
    "plt.plot([CI[1], CI[1]], [0,0.05], '--', color=\"black\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice: the simulated median are based on a distribution in wich the sample average is used to calculate the parameter lamb. \n",
    "\n",
    "The simulation uses the sample mean - not the sample median. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example: CI for Q3 from normal distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 161,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Lets calcualte the 99% CI for Q3 in the student height data:\n",
    "\n",
    "x = np.array([168, 161, 167, 179, 184, 166, 198, 187, 191, 179])\n",
    "# we assume that the data come from an underlying normal distribution\n",
    "\n",
    "n = len(x)\n",
    "k = 100000\n",
    "\n",
    "# simmulate k samples of size n (from normal distribution)\n",
    "sim_samples = stats.norm.rvs(size=(n,k), loc=x.mean(), scale=x.std(ddof=1)) # note mean and std are matched to data\n",
    "\n",
    "# calculate Q3 in each sample\n",
    "sim_Q3 = np.percentile(sim_samples, 75, axis=0)\n",
    "\n",
    "# lets visualise all the simulated Q3 values:\n",
    "plt.hist(sim_Q3)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 162,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[172.8729571 198.0447535]\n"
     ]
    }
   ],
   "source": [
    "# now we find the 99% confidence interval:\n",
    "CI = np.percentile(sim_Q3, [0.5,99.5], axis=0)\n",
    "print(CI)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example: Simulation of difference between two samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 163,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# We image data from call center - now from two different days. \n",
    "# We want to know is there is a significant difference in average \n",
    "# waiting time between calls for the two days. \n",
    "\n",
    "# Data day 1\n",
    "x = np.array([32.6, 1.6, 42.1, 29.2, 53.4, 79.3, 2.3 , 4.7, 13.6, 2.0])\n",
    "n1 = len(x)\n",
    "\n",
    "# Data day 2\n",
    "y = np.array([9.6, 22.2, 52.5, 12.6, 33.0, 15.2, 76.6, 36.3, 110.2, 18.0, 62.4, 10.3])\n",
    "n2 = len(y)\n",
    "\n",
    "# always visualise :-)\n",
    "plt.hist(x, alpha=.5)\n",
    "plt.hist(y, alpha=.5)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will assume that both samples come from underlying exponential distributions (but with different means)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 164,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# simulate k samples of size n1 and n2\n",
    "\n",
    "k = 100000\n",
    "\n",
    "x_sim = stats.expon.rvs(size=(n1,k), scale=x.mean())\n",
    "y_sim = stats.expon.rvs(size=(n2,k), scale=y.mean())\n",
    "\n",
    "x_means = x_sim.mean(axis=0)\n",
    "y_means = y_sim.mean(axis=0)\n",
    "\n",
    "diffs = x_means - y_means\n",
    "\n",
    "plt.hist(diffs)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 165,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-40.22521509  14.10483978]\n"
     ]
    }
   ],
   "source": [
    "# find 95% confidence interval for the difference\n",
    "CI = np.percentile(diffs, [2.5, 97.5], method=\"averaged_inverted_cdf\")\n",
    "print(CI)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example: Womens cigarete consumption "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 176,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 3 13  7  5  6  0 -2 -4 -1 22  9]\n",
      "5.2727272727272725\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "before = np.array([8, 24, 7, 20, 6, 20, 13, 15, 11, 22, 15])\n",
    "after  = np.array([5, 11, 0, 15, 0, 20, 15, 19, 12, 0, 6])\n",
    "\n",
    "diff = before - after\n",
    "print(diff)\n",
    "print(diff.mean())\n",
    "\n",
    "plt.hist(diff)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This time we do not want to assume any underlying distribution - so we will do a non-parametric bootstrap"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 175,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 6  0 13 13 22]\n",
      " [ 7  0  9 22  5]\n",
      " [-1 13  6 -1 -1]\n",
      " [ 3 -2 -2 13  9]\n",
      " [ 5  5  0  9  9]\n",
      " [ 6  3  5  7  0]\n",
      " [ 6  3  9 -1  0]\n",
      " [22 -2 -2 -4 -4]\n",
      " [ 9 -2  9  0  5]\n",
      " [ 3 -1 13 -1 -4]\n",
      " [ 6 -2  7 -4  7]]\n"
     ]
    }
   ],
   "source": [
    "# First lets try to simulate 5 more samples by re-sampling the original data:\n",
    "\n",
    "sim_data = np.random.choice(diff,size=(len(diff), 5))\n",
    "print(sim_data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The simulated samples can only include the values in the original data (3, 13, 7, 5, 6, 0, -2, -4, -1, 22, 9)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 192,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.36363636 9.81818182]\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Now simulate MANY more samples (by re-sapling the original data many times):\n",
    "k = 100000\n",
    "sim_data = np.random.choice(diff,size=(len(diff), k))\n",
    "\n",
    "# calculate mean of each re-sample:\n",
    "sim_means = sim_data.mean(axis=0)\n",
    "\n",
    "# caluclate 95% CI from re-sampled samples:\n",
    "CI = np.percentile(sim_means, [2.5, 97.5], method=\"averaged_inverted_cdf\")\n",
    "print(CI)\n",
    "\n",
    "# always visualise :-)\n",
    "plt.hist(sim_means, density=True)\n",
    "plt.plot([CI[0], CI[0]], [0,.2], '--', color=\"black\")\n",
    "plt.plot([CI[1], CI[1]], [0,.2], '--', color=\"black\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We could also calculate the CI for the median (or other statistics)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 196,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-1.  9.]\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sim_medians = np.median(sim_data, axis=0)\n",
    "CI = np.percentile(sim_medians, [2.5, 97.5], method=\"averaged_inverted_cdf\")\n",
    "print(CI)\n",
    "\n",
    "plt.hist(sim_medians, density=True)\n",
    "plt.plot([CI[0], CI[0]], [0,.2], '--', color=\"black\")\n",
    "plt.plot([CI[1], CI[1]], [0,.2], '--', color=\"black\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example: Teeth and bottle-feeding (vs breast-feeding)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 199,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-6.21111111 -0.14444444]\n"
     ]
    }
   ],
   "source": [
    "# data from breastfed\n",
    "x = np.array([9, 10, 12, 6, 10, 8, 6, 20, 12])\n",
    "\n",
    "# data from bottlefed\n",
    "y = np.array([14,15,19,12,13,13,16,14,9,12])\n",
    "\n",
    "# Make simulations:\n",
    "k = 100000\n",
    "\n",
    "sim_x = np.random.choice(x,size=(len(x),k))\n",
    "sim_y = np.random.choice(y,size=(len(y),k))\n",
    "\n",
    "# calculate difference of means in simulated data:\n",
    "sim_mean_dif = sim_x.mean(axis=0) - sim_y.mean(axis=0)\n",
    "\n",
    "# calculate 95% CI:\n",
    "CI = np.percentile(sim_mean_dif, [2.5, 97.5], method=\"averaged_inverted_cdf\")\n",
    "print(CI)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 200,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-8.  0.]\n"
     ]
    }
   ],
   "source": [
    "# we could also fint the 99% CI for the difference of medians:\n",
    "sim_median_dif = np.median(sim_x,axis=0) - np.median(sim_y,axis=0)\n",
    "\n",
    "CI = np.percentile(sim_median_dif, [.5, 99.5], method=\"averaged_inverted_cdf\")\n",
    "print(CI)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "pernille",
   "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": "3.11.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}