statistics.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "from scipy import stats\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "rv = stats.expon(scale=3.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "r = rv.rvs(size=1000) + stats.norm(scale=0.01).rvs(size=1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot(rv, r):\n",
    "    x = np.linspace(rv.ppf(0.01), rv.ppf(0.99), 100)\n",
    "    fig, ax = plt.subplots(1, 1)\n",
    "    ax.plot(x, rv.pdf(x), 'r-', lw=5, alpha=0.6, label='expon pdf')\n",
    "    ax.hist(r, density=True, histtype='stepfilled', alpha=0.2)\n",
    "    ax.legend(loc='best', frameon=False)\n",
    "    plt.show();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
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       "        1.49429716e+00,  5.77057784e+00,  2.44507692e+00,  8.31906911e+00,\n",
       "        3.02171512e+00,  1.46520573e+01,  4.25064580e-01,  1.16204456e+00,\n",
       "        6.23561459e+00,  6.81176806e-02,  6.63806532e+00,  6.70062436e-01,\n",
       "        2.97257760e+00,  1.43574818e+00,  2.42516565e-01,  5.66810695e-01])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 1)\n",
    "ax.hist(r, density=True, histtype='stepfilled', alpha=0.2)\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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nvP8sVgB3B9t6lcaJkyA3ckqEoo06p15E0l9u54uAc+5F4MWwtjtCns84zrq/AX7T3QLTgSsqonHiWRStrmzXXly5nMZJkROgiYikE10ZG6P6c86NaCvYsR3fwV73B4qIZBkFfYyaR4yitWxQ+0bnKK58NzUFiYjESEEfKzPqK6ZFNBdXvqvbDIpIWlPQd0HD2eeAtb80wHf4EIVbN6WoIhGRzinou6CtX3/8Y8On+YE+776dgmpERGKjoO+i+nMviGgr2LoZ9u9PQTUiIp1T0HdR05hxtPYPm4DTOXjzzdQUJCLSCQV9V+Xk0DD1vMj2N9+E1tbk1yMi0gkFfTfUV0wDC9t0R47A6tWpKUhE5DgU9N3QVtov6s3DWbYs+cWIiHRCQd9NR8+/KLKxqgp2a/piEUkvCvpuah4xisCJJ0V2aK9eRNKMgr67zDh6/vTI9vfeg/r65NcjItIBBX0PNE6agissat/Y0gKvv56agkREolDQ94ArKIg6/w3LlkEgkPyCRESiUND3UP0F0yPmv+HwYaisjL6CiEiSKeh7qHXAQBrPOCuy409/8q6YFRFJMQV9HBy98JLIxt27Ydu2pNciIhJOQR8HLcOGw8iRkR1Let190EUkAyno42VGlNvmbtwINTXJr0VEJISCPl4mT4by8sh27dWLSIop6OMlJwdmzoxsr6yEffuSX4+ISJCCPp7OOw9KStq3tbXByy+nph4REWIMejObZWZbzazKzG6P0j/dzFaZWcDMrg3razWzNcHH4ngVnpby8uCyyyLb33oLDh1Kfj0iIsQQ9GbmA+4DrgQmANebWfiNUz8Avgr8LspLNDrnJgUfs3tYb/q7+GIoLGzfFghor15EUiaWPfqpQJVzbqdzrhlYCMwJXcA5V+2cWwe0JaDG3qW4GC69NLL99dehri759YhI1osl6AcDoZOs1wTbYlVoZpVmttzMro62gJndFFymsra2tgsvnaZmzID8/PZtLS3wyiupqUdEslosQW9R2rpybf+pzrkK4AbgXjMbFfFizj3snKtwzlWURztFsbfp29cbwgm3bJn26kUk6WIJ+hpgaMj3Q4A9sb6Bc25P8OtO4FVgchfq671mzvQOzoZqboY//jE19YhI1ool6FcAo81shJnlA3OBmM6eMbMBZlYQfD4IuADY1N1ie5XS0uh79a+95s1uKSKSJJ0GvXMuACwAlgCbgSedcxvN7G4zmw1gZueYWQ1wHfCQmW0Mrj4eqDSztcAy4KfOuewIeoArrog+Vv/SS6mpR0SyUm4sCznnXgReDGu7I+T5CrwhnfD13gYm9rDG3qu01DsDJ3wahDfegMsvh7Ky1NQlIllFV8Ym2syZUFDQvi0QgMWZfe2YiKQPBX2i9e0bfWbLd9/VzJYikhQK+mSYOdML/FDOwfPPp6YeEckqCvpkKCyEq66KbF+/HrZuTX49IpJVFPTJcvHF0Q++PvWU7i0rIgmloE+W3FyYMyeyffduWL48+fWISNZQ0CfT1KkwbFhk+/PPQ1NT8usRkaygoE8mM7juusj2Q4c0NYKIJIyCPtlGj4ZJkyLbX35ZtxwUkYRQ0KfCl77kjdmHCgTgySdTU4+IZLSYpkCQzq2v6cpEZQWUTjqPvq8tbd/89gr2j11O09jxXXrviUP6dWl5Ecku2qNPkbrPzaStNDKg+//vM97EZyIicaKgTxFXUMDhKyNvoes7sI+SV/+UgopEJFMp6FOocdLZNI+IuOEWJa8uJbd2bwoqEpFMpKBPJTMOXX0d5Pjat7cG6P/sIl0xKyJxoaBPscCJJ3F0+qUR7fm7dlD83jspqEhEMo2CPg3UfW4mrQMi58Hp99Jicg4fSkFFIpJJFPRpwOXnc+iav4xoN7+f/s9p0jMR6RkFfZpoGj2WhilTI9oLt2ykaHVlCioSkUyhoE8jhz8/h7a+JRHt/Rc/oyEcEek2BX0accV9OHT1tRHt5vcz4JmFGsIRkW5R0KcZ/xln0Tjp7Ij2gm1b6PPOGymoSER6OwV9Gjo0+0u0lZRGtPf7w2JyP/4oBRWJSG8WU9Cb2Swz22pmVWZ2e5T+6Wa2yswCZnZtWN88M9sefMyLV+GZzBX34eCX5kZ2tAYYuPBxzYUjIl3SadCbmQ+4D7gSmABcb2YTwhb7APgq8LuwdQcCdwLTgKnAnWY2oOdlZ76mcROoP/fCiPbcj/fQ7w//m4KKRKS3imWPfipQ5Zzb6ZxrBhYC7W5+6pyrds6tA9rC1r0CeMU5d8A5dxB4BZgVh7qzwpGrZhMoPyGivc/yNylcvyYFFYlIbxRL0A8Gdod8XxNsi0VM65rZTWZWaWaVtbW1Mb505nP5+Ry8/q/BF3nbgAHPLMR3YH8KqhKR3iaWoLcobbGe5xfTus65h51zFc65ivLy8hhfOju0nDKEw5+PnM7Y/H4GPv4bjdeLSKdiCfoaYGjI90OAPTG+fk/WlaD68y7CP2FiRHveRx/S/3lNkSAixxdL0K8ARpvZCDPLB+YCi2N8/SXATDMbEDwIOzPYJl1hxsHrrqe1/8CIruKV78EbOr9eRDrWadA75wLAAryA3gw86ZzbaGZ3m9lsADM7x8xqgOuAh8xsY3DdA8A/4f1nsQK4O9gmXeSKijlw41ejjtfz+9/D9u1Jr0lEegdzafZnf0VFhaus7P4kXl27SXfvU/zeO95NSUKU9cmHkhL4wQ+gLHK6YxHJfGa20jlXEa1PV8b2Mg1Tz6PhnHMjO+rq4L77wO9PflEiktYU9L3QoTnX0jxsRGTHhx/Cf/4ntIVfziAi2UxB3xvl5nLgxq/RVtovsm/DBlik+82KyGcU9L1UW0kp++d9A5eXF9n56quwRCc3iYhHQd+LtQwe6l05a1GuS3vuOXhHNxcXEQV9r+efMBGujbxZCQCPPQZr1ya3IBFJOwr6TDBjhvcI19YGDz8MW7YkvyYRSRsK+kxx7bVQEeUU2kAA7r8fduxIfk0ikhYU9JnCDL72NRg/PrKvqQl+9Suork56WSKSegr6TJKbCzffDCNHRvb5/XDvvbBrV/LrEpGUUtBnmoIC+Pa3YciQyL7GRi/sNYwjklUU9JmouBi+9z045ZTIPr8f/v3fdYBWJIso6DNVSQnccgucfHJkX1MT/Md/wOrVya9LRJJOQZ/JSkvh1luj79kHAvDQQ/DWW8mvS0SSSkGf6Y6FfbQxe+e8i6r+7/80N45IBlPQZ4OSEvj7v4dRo6L3v/CCF/iBQHLrEpGkUNBni+Ji+O534fTTo/e//bZ3kLa+Prl1iUjCKeizSUEB/N3fwbRp0fu3bYOf/AT26P7tIplEQZ9tcnO9K2ivuCJ6f20t/PSnOiNHJIMo6LORGVxzDdx4I+RE+Qg0NcGDD8Kzz+puVSIZQEGfzS66CL7zHSgqit6/ZAn827/BoUPJrUtE4kpBn+3Gj4cf/jD6hVXgjdv/+MewcWNy6xKRuFHQC5xwAtx+O5x1VvT+ujpv9ssnn4SWluTWJiI9FlPQm9ksM9tqZlVmdnuU/gIzWxTsf9fMhgfbh5tZo5mtCT4ejG/5EjeFhd7Ml1dfHf3WhABLl8I//zPs3p3c2kSkR3I7W8DMfMB9wOVADbDCzBY75zaFLPZ14KBz7jQzmwv8DPhysG+Hc25SnOuWEOtrDsfvxSaeT0HRIAYsfJyco3WR/dur4Yd3UXfZTIbf+CXvLB4RSWux7NFPBaqcczudc83AQmBO2DJzgEeDz58GLjPraLdQ0l3TaWPY+93/R9PosdEXcG2U/OmP3t69bmYikvZiCfrBQOjf6jXBtqjLOOcCwGGgLNg3wsxWm9lrZnZRtDcws5vMrNLMKmtra7v0D5DEaCspZf/fzOfw568GXwd77R9+6J1zv2iRN/2xiKSlWII+2p55+AxYHS3zEXCqc24ycCvwOzMrjVjQuYedcxXOuYry8vIYSpKkMKP+okvYu+AWAidFmQETvMnQ/vxnuOMOWLFCk6OJpKFYgr4GGBry/RAg/Br5T5cxs1ygH3DAOdfknNsP4JxbCewAxvS0aEmuwMmD2bvgVuouvRysg4/M4cPwX/8Fv/ylDtaKpJlYgn4FMNrMRphZPjAXWBy2zGJgXvD5tcCfnXPOzMqDB3Mxs5HAaGBnfEqXpMrNpe6Kz1O74BZaTg4fuQuxfTvccw88+qgutBJJE50GfXDMfQGwBNgMPOmc22hmd5vZ7OBi/w2UmVkV3hDNsVMwpwPrzGwt3kHa+c65A/H+R0jytAweSu2CWzky6y8gPz/6Qs55s2H+wz/A889DQ0NyixSRdsyl2ZhqRUWFq6ys7Pb6cT3VUI5rYlHAOxC7du3xFywuhpkz4XOf82bQFJG4M7OVzrmKaH26Mla6r6zMm/b429+GE0/seLmGBm/P/oc/hJde0hk6Ikmmq12k5844A8aNg9de825L2NFQzdGjXuC//DJceqn3KClJbq0iWUhBL/GRmwuXXQbnnuvttS9b1vGtCRsa4A9/8AL/vPNgxozj/0UgIj2iMXpJCN/Bg5Qs/SPFK1eA63xO+6ax4zl6/nSaxozreK6doIlD+sWrTJGMcbwxeu3RS0K0DhjAoWuvp+6SGZQuXULRmlXHDfyCrZsp2LqZ1oGDqJ96Hg0VU2nrq2EdkXjQHr0khW//Pkpe/ZO3h9/W2vkKOT78E86gvmKat5cfcics7dGLRNIevaRca9kgDn1pLkdmzKLvW6/R5923saamjldoa6Vww1oKN6ylraSUhslTaJw05fgXa4lIVNqjl5Qwv5/iynfp++Zr+A7Ffg1d4IQTOfFzF8KUKR3fFUskCx1vj15BL6nV1kbh1k30efsNCrZvjWmVsj7BK3JPOQUmT4ZJk2Do0E4P4opkMg3dSPrKycE//gz848/At38ffd57m+KVK6Lf9CTcnj3e4w9/gAEDvFshTpwIY8dCXl7iaxfpJbRHL+mntZXCrZsoXrmCws0bIw7efrpH35G8PBgzBiZM8B4nn6y9fcl42qOX3sXnwz9hIv4JE7GGeorXrqZo7Sryq2Oc+LSlBTZu9B4ApaXeXv6xR3m5gl+yioJe0por7kP9eRdSf96F+A4epHDDWlrWrSZv9/uxv0j9PvhoH7z6FgBtfUtoGjGK5mEjaB423DuTJ8Z73+rUTumNFPTSa7QOGED9RZdQf9El5Bw6RNGmdRRuXE/Bzh0xXX17TM7ROorWr6Fo/RqvITeP5sFDaB46jJahw2geMpTWgWXa65eMoaCXXqmtf3/qz59O/fnTscYGCrdtpXDLRgq2bSGn/mjXXizQQv77u8h/f9enTa6wiJaTT6F58FBaThlMy8mnECjXfDzSOynopddzRcU0njWZxrMmg3Pk7amhYNsWCqq2UVC9C1o7mFztOMzfSP6uHeTv2vFZY44PRg2FwYO9UztPPhlOOglOOAF8vvj9g0TiTEEvmcWMlsFDaRk8lKOXXg4tLRS8v4v8Hdsp2LWT/N3vdyv4AWhrZf/2atheHfaeOQTKyggMOoFA+QkEygbROqjc+9qvf7vpG7pLxwakJxT0ktny8mg6bQxNp42hDqClhfyaD8iv9oZq8j+oJqehvmfv4drI3VdL7r5a2LKxfV+Oj9YBAwgMLKN1YBmB/gNpHTCQ1v4DCPQfQFtpaVz+IxA5HgW9ZJe8PJpHjKJ5xCjve+fwHdhP/u4PyN/9Pnkf7ibvw91YS0t83q+tFd/+ffj274vebzm0lpbS2q8/baX9aD326NePtpJSWvuW0FpaCq5UB4el2xT0kt3MaC0bRGPZIBonne21tbWRW7uXvD0fkvdRDXkf7SHvoz2xXa3bVa4N3+FD+A4fOv5ypUXe9QAlJd7Xvn295yUl3vNjjz59PnvoLwUJUtCLhMvJIXDiSQROPInGyVM+az5aR+4nH5O392NyPw5+rd2bmP8AwrW2wsGD3iNWhYVe4BcXt38UFUU+Cgs/+3rsUVCgvyIyhIJeJEZtfUto7ltC86jR7dqtsYHc2r2fjtPn7qsld/8+cvfvw/yNKaoW7ybsfj/s39/918jP/yz0jz3y871bQE6bFr9aJaEU9CI95IqKaTl1OC2nDo/os8YGcg/sx3fwALkHDuA7eADfoYP4Dh0k9xn/flEAAAdCSURBVNBBrLGDG6mni+Zm7xFu7Njk1yLdFlPQm9ks4N8BH/BfzrmfhvUXAI8BU4D9wJedc9XBvh8AXwdage8455bErXqRNOeKimkZXEzL4KFR+625+dMx+pwjh/EdPoyv7gi+I4fJqTuC78gRcuqTMDTUVfmdTCwnaaXToDczH3AfcDlQA6wws8XOuU0hi30dOOicO83M5gI/A75sZhOAucDpwCnAn8xsjHMuhnvJiWQ+l5/vnXtffsJxl/u4qYmco3XkHD2Kr977mlN/lJz6enz1R8lpqCenvp6chgZyGuqxJj8kcGbaQ0cCNCR4pthUXjuQqllwE/VvjmWPfipQ5ZzbCWBmC4E5QGjQzwHuCj5/Gvi1mVmwfaFzrgnYZWZVwdd7Jz7li2QHV1BAa0EBrWWDiOnEz7Y2zN/oBX9jAzmNjeQ0NmKNDeT4/eT4G7GmJu+r309Ok/+zr01NWHMTFm3I5lg9edqj701iCfrBwO6Q72uA8KMwny7jnAuY2WGgLNi+PGzdiJt+mtlNwE3Bb4+aWWy3GopuENDBScspla51QfrWprq6Ljm1PfFIV9fQNuu6rtY1rKOOWII+2vlV4X8TdrRMLOvinHsYeDiGWjplZpUdTb6fSulaF6Rvbaqr69K1tnStC9K3tnjWFcsVFTVA6JGkIcCejpYxs1ygH3AgxnVFRCSBYgn6FcBoMxthZvl4B1cXhy2zGJgXfH4t8Gfn3aNwMTDXzArMbAQwGngvPqWLiEgsOh26CY65LwCW4J1e+Rvn3EYzuxuodM4tBv4beDx4sPUA3n8GBJd7Eu/AbQD4VhLOuInLEFACpGtdkL61qa6uS9fa0rUuSN/a4lZX2t0cXERE4kuzHomIZDgFvYhIhuu1QW9ms8xsq5lVmdntUfoLzGxRsP9dMxuehJqGmtkyM9tsZhvN7LtRlrnEzA6b2Zrg445E1xXy3tVmtj74vpVR+s3MfhXcZuvM7Owk1DQ2ZFusMbMjZva9sGWSts3M7DdmttfMNoS0DTSzV8xse/DrgA7WnRdcZruZzYu2TJzr+oWZbQn+rJ4zs/4drHvcn3sC6rrLzD4M+Xld1cG6x/0dTlBti0LqqjazNR2sm8htFjUnEvo5c871ugfeQeEdwEggH1gLTAhb5u+AB4PP5wKLklDXycDZweclwLYodV0C/F+Ktls1MOg4/VcBL+Fd/3Au8G4Kfq4fA8NStc2A6cDZwIaQtp8Dtwef3w78LMp6A4Gdwa8Dgs8HJLiumUBu8PnPotUVy889AXXdBXw/hp/1cX+HE1FbWP8vgTtSsM2i5kQiP2e9dY/+02kZnHPNwLFpGULNAR4NPn8auMwssZNrO+c+cs6tCj6vAzYT5UrgNDYHeMx5lgP9zezkJL7/ZcAO59z7SXzPdpxzr+OdORYq9LP0KHB1lFWvAF5xzh1wzh0EXgFmJbIu59zLzrljN8BdjnedSlJ1sL1iEcvvcMJqC2bBXwK/j+d7xuI4OZGwz1lvDfpo0zKEB2q7aRmAY9MyJEVwqGgy8G6U7vPMbK2ZvWRmpyerJryrkl82s5XmTTsRLpbtmkhz6fgXL1XbDOBE59xH4P2SAtFmIEv1tvsbvL/Gouns554IC4JDSr/pYAgi1dvrIuAT59z2DvqTss3CciJhn7PeGvQ9mZYh4cysL/AM8D3n3JGw7lV4QxNnAf8BPJ+MmoIucM6dDVwJfMvMpof1p3Kb5QOzgaeidKdym8UqldvuR3jXqTzRwSKd/dzj7QFgFDAJ+AhviCRcyrZX0PUcf28+4dusk5zocLUobZ1ut94a9D2ZliGhzCwP74f3hHPu2fB+59wR59zR4PMXgTwzG5TouoLvtyf4dS/wHN6fz6FSOWXFlcAq59wn4R2p3GZBnxwbwgp+3RtlmZRsu+DBuC8AX3HBQdxwMfzc48o594lzrtU51wb8Zwfvl7LPWjAPrgEWdbRMordZBzmRsM9Zbw36nkzLkDDBcb//BjY75/61g2VOOnaswMym4v0MenCvt5hr62NmJcee4x3I2xC22GLgr81zLnD42J+SSdDhHlaqtlmI0M/SPOB/oyyzBJhpZgOCQxUzg20JY94NgW4DZjvnot6qKsafe7zrCj2u88UO3i+W3+FEmQFscc7VROtM9DY7Tk4k7nOWiKPKyXjgnSGyDe/I/Y+CbXfjfegBCvGGAarw5tcZmYSaLsT7M2odsCb4uAqYD8wPLrMA2Ih3lsFy4Pwkba+RwfdcG3z/Y9sstDbDu8nMDmA9UJGk2orxgrtfSFtKthnefzYfAS14e09fxzu2sxTYHvw6MLhsBd4d146t+zfBz1sV8LUk1FWFN1577LN27CyzU4AXj/dzT3Bdjwc/P+vwwuvk8LqC30f8Die6tmD7I8c+WyHLJnObdZQTCfucaQoEEZEM11uHbkREJEYKehGRDKegFxHJcAp6EZEMp6AXEclwCnoRkQynoBcRyXD/H4YAdzlMunisAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(stats.expon(scale=r.mean()), r)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "KstestResult(statistic=0.029170951878874196, pvalue=0.3576732533605639)"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.kstest(r, stats.expon(scale=r.mean()).cdf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.054528078840026"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-0.012229644524133063, 3.066757723364159)"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.expon.fit(r)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "rv = stats.expon(-0.012229644524133063, 3.066757723364159)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "KstestResult(statistic=0.028948318063856338, pvalue=0.36710612944696597)"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.kstest(r, rv.cdf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(rv, r)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "log_r = np.log(0.5 + r)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 2.34810413e+00,  8.46116104e-01,  5.14087903e-01,  1.44941432e+00,\n",
       "        1.62490432e-01, -4.58713147e-01,  8.08774390e-01,  7.10375414e-01,\n",
       "        3.18513837e-01,  1.66135205e+00,  4.00872781e-01,  1.52180475e+00,\n",
       "        7.24995969e-01,  4.28718220e-01,  3.50912684e-01,  4.16244728e-01,\n",
       "        7.87871739e-01,  1.89029069e+00,  9.61538022e-01,  3.61853511e-01,\n",
       "        8.15569980e-01,  1.70312480e+00,  1.58106377e-01,  1.96130203e+00,\n",
       "        4.61209211e-01,  4.42329606e-01,  2.43898556e+00,  6.50119663e-01,\n",
       "       -3.51605733e-01,  1.30270570e+00,  1.71670974e+00,  1.68091450e+00,\n",
       "        1.62905077e+00,  9.81622861e-01,  5.29366312e-01,  1.32965387e-01,\n",
       "        1.77618292e+00,  1.75147926e+00,  2.40020443e+00,  1.64855047e+00,\n",
       "        1.18589163e+00, -6.51144830e-01,  7.79211541e-01, -1.69923928e-01,\n",
       "        1.15522136e+00,  6.45484845e-01,  1.73165304e+00,  1.20219580e+00,\n",
       "        1.69291444e+00, -5.42411128e-01,  1.13611603e+00,  8.04175683e-01,\n",
       "        6.24072569e-01,  2.28118257e+00,  3.49299944e-01,  2.20011021e-01,\n",
       "        1.74089828e-01,  2.16040343e+00,  8.80611819e-01,  4.86699213e-01,\n",
       "        1.14338220e+00,  6.28448727e-01,  1.61369697e+00,  1.87171644e+00,\n",
       "        1.87666090e+00,  3.09576932e-01,  1.41121417e+00,  1.03580516e+00,\n",
       "        6.22711526e-01,  1.26468833e+00,  6.96929153e-01,  1.09489986e-01,\n",
       "        7.18488469e-01,  1.77118826e+00,  9.38085159e-01,  2.26382353e+00,\n",
       "       -7.17910567e-01,  1.23141806e+00,  2.24457081e+00,  1.08790096e+00,\n",
       "        8.13771688e-01,  1.00678101e+00,  1.90183727e+00,  8.48475182e-02,\n",
       "        9.37110022e-01,  5.81824145e-01,  1.22264101e+00,  1.03528759e+00,\n",
       "        2.63649674e+00, -5.35548508e-01,  1.61349818e+00,  1.99041262e+00,\n",
       "        6.74702364e-01,  6.91552996e-02,  1.03555427e+00,  1.94120664e+00,\n",
       "        1.44891119e+00,  2.04651419e-01, -3.66822153e-01,  1.73951745e-01,\n",
       "        4.61438298e-01,  3.95847490e-01,  1.77197883e+00,  1.83527990e+00,\n",
       "        4.18353047e-01,  1.80215459e+00,  3.06220913e-01,  2.01073453e+00,\n",
       "        1.47642612e+00,  2.31086200e+00,  1.34517093e+00, -2.63883140e-01,\n",
       "        9.86551995e-01,  2.92308565e+00, -5.94047960e-01,  9.88131873e-01,\n",
       "        7.18505261e-01,  1.99067311e+00,  1.40981378e+00,  3.63433505e-02,\n",
       "        1.53290607e-01,  1.10742858e+00,  1.95789875e+00,  8.02942086e-01,\n",
       "        2.44782182e+00,  4.38885531e-01,  5.11815704e-01,  8.09346623e-01,\n",
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       "        1.63432641e+00,  8.87495273e-01,  1.20445216e+00, -4.23590917e-02,\n",
       "       -3.53100813e-01,  4.85168837e-01,  1.35680275e+00, -6.23330448e-01,\n",
       "       -4.35039580e-01,  2.32320127e+00, -5.42812729e-01,  1.46538767e+00,\n",
       "        5.25837237e-01,  2.13332859e+00,  1.19819331e+00,  1.61905219e-01,\n",
       "       -3.25605240e-01,  1.48913694e+00,  1.54159306e+00,  1.50009938e+00,\n",
       "       -5.99175899e-02,  3.70604560e-01,  1.84371605e+00,  1.32936054e+00,\n",
       "        1.42316235e+00,  9.98248652e-01,  1.65020536e+00,  8.35024325e-01,\n",
       "        8.22533016e-01,  3.83664771e-01,  6.41441917e-01,  1.38485608e+00,\n",
       "        1.47264911e-03,  1.46877517e+00,  2.58267410e+00,  6.77421417e-01,\n",
       "        1.21479124e+00,  1.27999431e+00,  5.10304503e-02,  6.56557533e-01,\n",
       "        1.33733342e+00,  9.03658204e-01,  3.48323059e-01,  1.49104577e+00,\n",
       "        1.20111981e+00,  1.35733153e+00, -1.38382441e-01,  2.00158270e+00,\n",
       "        1.62740207e+00,  1.78928864e+00, -4.45824987e-01,  1.97211991e+00,\n",
       "        1.84959818e+00,  4.70409435e-01,  9.93484869e-01, -1.11054148e-01,\n",
       "        7.19243392e-02,  1.69548607e+00,  4.06567597e-01, -4.57598014e-01,\n",
       "        3.75261830e-01,  1.30783075e+00,  6.62101410e-01, -3.82416894e-01,\n",
       "        4.68756685e-01,  9.12449253e-01,  1.46626264e+00,  1.37802538e+00,\n",
       "        1.12379965e+00,  1.02027383e+00,  9.34246098e-01,  1.54219034e+00,\n",
       "        6.07325173e-01,  4.06649023e-01,  5.49670401e-01,  2.74829495e-01,\n",
       "       -3.58499808e-01,  1.47115794e+00,  1.31734715e+00,  2.12911208e+00,\n",
       "        1.35661234e+00,  1.67136973e+00, -3.94992431e-01,  4.10657408e-02,\n",
       "       -2.44442073e-01,  3.49757829e-01,  1.27985332e+00,  2.48433124e+00,\n",
       "        1.24766435e-01, -4.03516935e-01, -3.65955001e-01,  1.56302849e-01,\n",
       "       -3.84222770e-01,  2.10261100e+00,  1.35378969e+00,  5.91580024e-01,\n",
       "        1.52646407e+00,  1.82537639e-02, -5.87499010e-02,  6.47363521e-01,\n",
       "        1.04327979e+00,  3.25471970e-01,  1.31559000e+00,  2.65139604e+00,\n",
       "        7.93742696e-01,  1.23526376e+00, -1.81557643e-01, -2.13870446e-02,\n",
       "        1.66835881e+00,  3.79643517e-01,  4.66532382e-01,  1.27536753e+00,\n",
       "        2.37026049e+00,  2.17829394e+00,  8.53736394e-01,  2.51128251e+00,\n",
       "        6.57114593e-01, -3.14699753e-01,  1.14694578e+00,  5.09106472e-01,\n",
       "        2.15226750e-01, -2.75893221e-01,  1.41530906e+00,  2.23963294e+00,\n",
       "        1.54720853e+00,  1.21884136e+00,  1.47895693e+00,  1.04820860e+00,\n",
       "        1.68893977e+00,  3.18141172e-01,  8.34260605e-01,  1.11288649e+00,\n",
       "        1.06557701e+00,  1.42658298e+00,  7.82018439e-01,  1.86494691e+00,\n",
       "        4.43712693e-01,  9.00525828e-01,  8.84161752e-01,  2.83008184e-01,\n",
       "        2.49840938e+00, -5.76420515e-01,  4.17732545e-01, -2.15592422e-01,\n",
       "        1.84895248e+00, -1.83063494e-02,  2.53810187e+00,  2.33845808e+00,\n",
       "       -2.80441922e-01,  1.31485653e+00,  1.95714886e-01,  5.22343827e-01,\n",
       "        1.11725703e+00,  2.94262717e-01,  1.33863602e+00,  1.24060129e+00,\n",
       "        2.29563498e+00,  2.04407008e+00,  8.13209265e-01,  2.70961680e+00,\n",
       "       -7.97945018e-02,  1.66899444e+00,  1.12738693e+00,  2.53220188e-01,\n",
       "        4.21976322e-01,  2.08902286e+00,  1.94504220e+00,  1.83964721e-01,\n",
       "        8.02901016e-01, -4.98890159e-01,  3.84358415e-01,  1.06576479e+00,\n",
       "        9.56731878e-01,  1.80303508e+00,  1.03983028e+00,  1.37223933e+00,\n",
       "        1.77456770e+00,  2.20178458e+00,  9.94375657e-01,  1.36749108e+00,\n",
       "        1.66865407e+00,  1.91879418e+00,  1.48318031e+00,  2.44007067e+00,\n",
       "        6.90291688e-01,  1.83586851e+00,  1.08013494e+00,  2.17691632e+00,\n",
       "        1.25894812e+00,  2.71813632e+00, -7.78917272e-02,  5.08048505e-01,\n",
       "        1.90740906e+00, -5.65426698e-01,  1.96544178e+00,  1.57057111e-01,\n",
       "        1.24489714e+00,  6.60493906e-01, -2.97710098e-01,  6.46735385e-02])"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "log_r"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 1)\n",
    "ax.hist(log_r, density=True, histtype='stepfilled', alpha=0.2)\n",
    "plt.show();"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}