{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "6e7869d6",
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy import stats\n",
    "import numpy as np\n",
    "\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "06efc6b0",
   "metadata": {},
   "outputs": [],
   "source": [
    "rep = 10**4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "9250660f",
   "metadata": {},
   "outputs": [],
   "source": [
    "def L(rep):\n",
    "    return stats.expon.rvs(size=rep,scale=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "5e21d937",
   "metadata": {},
   "outputs": [],
   "source": [
    "def N(t,Lvals):\n",
    "    s = 0\n",
    "    for i in range(len(Lvals)):\n",
    "        s = s+Lvals[i]\n",
    "        if s>t:\n",
    "            return i\n",
    "    return None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "b3c4faee",
   "metadata": {},
   "outputs": [],
   "source": [
    "L0 = L(rep)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "c7220838",
   "metadata": {},
   "outputs": [],
   "source": [
    "Nvals = [N(4,L(30)) for _ in range(rep)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "64cc5d55",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0, 1010.0)"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# An \"interface\" to matplotlib.axes.Axes.hist() method\n",
    "n, bins, patches = plt.hist(x=L0, bins='auto', color='#0504aa',\n",
    "                            alpha=0.7, rwidth=0.85)\n",
    "plt.grid(axis='y', alpha=0.75)\n",
    "plt.xlabel('Value')\n",
    "plt.ylabel('Frequency')\n",
    "plt.title('Waiting times')\n",
    "plt.text(23, 45, r'$\\mu=15, b=3$')\n",
    "maxfreq = n.max()\n",
    "# Set a clean upper y-axis limit.\n",
    "plt.ylim(ymax=np.ceil(maxfreq / 10) * 10 if maxfreq % 10 else maxfreq + 10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "33e9f7dc",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 167.    0.    0.    0.    0.  752.    0.    0.    0.    0. 1460.    0.\n",
      "    0.    0.    0.    0. 2036.    0.    0.    0.    0. 1908.    0.    0.\n",
      "    0.    0.    0. 1543.    0.    0.    0.    0. 1084.    0.    0.    0.\n",
      "    0.  556.    0.    0.    0.    0.    0.  298.    0.    0.    0.    0.\n",
      "  105.    0.    0.    0.    0.    0.   61.    0.    0.    0.    0.   22.\n",
      "    0.    0.    0.    0.    8.]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# An \"interface\" to matplotlib.axes.Axes.hist() method\n",
    "n, bins, patches = plt.hist(x=Nvals, bins='auto', color='#0504aa',\n",
    "                            alpha=0.7, rwidth=0.85)\n",
    "plt.grid(axis='y', alpha=0.75)\n",
    "plt.xlabel('Value')\n",
    "plt.ylabel('Frequency')\n",
    "plt.title('Waiting times')\n",
    "plt.text(23, 45, r'$\\mu=15, b=3$')\n",
    "maxfreq = n.max()\n",
    "# Set a clean upper y-axis limit.\n",
    "plt.ylim(ymax=np.ceil(maxfreq / 10) * 10 if maxfreq % 10 else maxfreq + 10)\n",
    "print(n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "a653fe36",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3.98, 3.9374)"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(Nvals), np.var(Nvals)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "9d11bce3",
   "metadata": {},
   "outputs": [],
   "source": [
    "Pvals = stats.poisson.rvs(size=rep,mu=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "ab2a755f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.890e+02 0.000e+00 0.000e+00 0.000e+00 0.000e+00 7.410e+02 0.000e+00\n",
      " 0.000e+00 0.000e+00 0.000e+00 1.448e+03 0.000e+00 0.000e+00 0.000e+00\n",
      " 0.000e+00 0.000e+00 1.983e+03 0.000e+00 0.000e+00 0.000e+00 0.000e+00\n",
      " 2.000e+03 0.000e+00 0.000e+00 0.000e+00 0.000e+00 0.000e+00 1.566e+03\n",
      " 0.000e+00 0.000e+00 0.000e+00 0.000e+00 1.016e+03 0.000e+00 0.000e+00\n",
      " 0.000e+00 0.000e+00 0.000e+00 5.810e+02 0.000e+00 0.000e+00 0.000e+00\n",
      " 0.000e+00 2.840e+02 0.000e+00 0.000e+00 0.000e+00 0.000e+00 0.000e+00\n",
      " 1.240e+02 0.000e+00 0.000e+00 0.000e+00 0.000e+00 4.700e+01 0.000e+00\n",
      " 0.000e+00 0.000e+00 0.000e+00 0.000e+00 1.600e+01 0.000e+00 0.000e+00\n",
      " 0.000e+00 0.000e+00 1.000e+00 0.000e+00 0.000e+00 0.000e+00 0.000e+00\n",
      " 4.000e+00]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# An \"interface\" to matplotlib.axes.Axes.hist() method\n",
    "n, bins, patches = plt.hist(x=Pvals, bins='auto', color='#0504aa',\n",
    "                            alpha=0.7, rwidth=0.85)\n",
    "plt.grid(axis='y', alpha=0.75)\n",
    "plt.xlabel('Value')\n",
    "plt.ylabel('Frequency')\n",
    "plt.title('Waiting times')\n",
    "plt.text(23, 45, r'$\\mu=15, b=3$')\n",
    "maxfreq = n.max()\n",
    "# Set a clean upper y-axis limit.\n",
    "plt.ylim(ymax=np.ceil(maxfreq / 10) * 10 if maxfreq % 10 else maxfreq + 10)\n",
    "print(n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "ab5f082f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3.98, 3.9374)"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(Nvals), np.var(Nvals)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "b2fba738",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "KstestResult(statistic=0.676, pvalue=0.0)"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.kstest(Pvals,Nvals)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f33fd314",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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