{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 生成泊松过程\n",
    "算法：首先生成一系列的指数分布，假设：$x_i\\sim E(0,1/\\lambda),i=0,1,...$，那么给定时间$t$，泊松分布可以由以下过程生成：$$ N(t)=\\arg \\min_t \\left\\{ \\sum _{i=0} ^{\\infty} x_i \\leq t \\right\\}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import numpy.random as nprd\n",
    "\n",
    "## 设定参数\n",
    "b=1.0/100 #指数分布参数,一个小时平均到达100次\n",
    "Nexp=2000 #生成足够多的指数分布\n",
    "\n",
    "## 生成N个x~F(x)=1-exp{-(1/b)*x}\n",
    "X=-b*np.log(nprd.random(Nexp))\n",
    "S=[]\n",
    "s=0\n",
    "# 产生累积和\n",
    "for x in X:\n",
    "    s=s+x\n",
    "    S.append(s)\n",
    "\n",
    "## 给定一些时间点，比如从第一分钟到敌五分钟，在这些点上计算到达的个数\n",
    "t=np.linspace(0.0,5.0/60,500) #0.1,0.3,...,9.9\n",
    "N=np.zeros(len(t))\n",
    "i=0\n",
    "for tt in range(len(t)):\n",
    "    while t[tt]>=S[i]:\n",
    "        i=i+1\n",
    "    N[tt]=i\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1b014ae358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## 导入matplotlib\n",
    "import matplotlib.pyplot as plt \n",
    "## 使图形直接插入到jupyter中\n",
    "%matplotlib inline\n",
    "# 设定图像大小\n",
    "plt.rcParams['figure.figsize'] = (15.0, 8.0)\n",
    "\n",
    "t_plot=[tt*60 for tt in t]\n",
    "plt.plot(t_plot,N,label=r'$Poisson Process$',color='blue')\n",
    "plt.legend(loc='upper left', frameon=True)\n",
    "plt.show() ## 画图"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 复合泊松过程\n",
    "算法：给定$N(t)$为一个泊松过程，现在假设$Z_j\\sim N(0,1)$，那么复合泊松过程为：$$M(t)=\\sum _{j=1} ^{N(t)} Z_j$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1b228c5780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 生成一系列正态分布\n",
    "Z=nprd.normal(0,1,int(N[-1]))\n",
    "SZ=[]\n",
    "s=0\n",
    "for z in Z:\n",
    "    s=s+z\n",
    "    SZ.append(s)\n",
    "\n",
    "# 生成复合泊松过程\n",
    "M=[]\n",
    "for n in N:\n",
    "    if int(n)==0:\n",
    "        M.append(0)\n",
    "    else:\n",
    "        M.append(SZ[int(n)-1])\n",
    "M=np.array(M)\n",
    "\n",
    "## 导入matplotlib\n",
    "import matplotlib.pyplot as plt \n",
    "## 使图形直接插入到jupyter中\n",
    "%matplotlib inline\n",
    "# 设定图像大小\n",
    "plt.rcParams['figure.figsize'] = (15.0, 8.0)\n",
    "\n",
    "t_plot=[tt*60 for tt in t]\n",
    "plt.plot(t_plot,M,label=r'$Compound Poisson Process$',color='blue')\n",
    "plt.legend(loc='upper left', frameon=True)\n",
    "plt.show() ## 画图"
   ]
  }
 ],
 "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": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}