Poisson_dist.ipynb

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    "%%javascript\n",
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   "source": [
    "# Visualisation\n",
    "import matplotlib as mpl\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.pylab as pylab\n",
    "import seaborn as sns\n",
    "\n",
    "# Configure visualisations\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
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    "ExecuteTime": {
     "end_time": "2017-09-11T20:42:18.615799",
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   "source": [
    "from math import pow, exp, factorial\n",
    "\n",
    "class Poisson:\n",
    "\n",
    "    def __init__(self, rate):\n",
    "        self.rate = rate\n",
    "\n",
    "    def prob_exactly(self, n, t):\n",
    "        rate = self.rate * t\n",
    "        return pow(rate, n) * exp(-rate) / factorial(n)\n",
    "\n",
    "    def prob_at_least(self, n, t):\n",
    "        complements = range(n)\n",
    "        total = 0.0\n",
    "\n",
    "        for c in complements:\n",
    "            p = self.prob_exactly(c, t)\n",
    "            total += p\n",
    "\n",
    "        return 1 - total\n",
    "\n",
    "    def prob_at_most(self, n, t):\n",
    "        return 1 - self.prob_at_least(n + 1, t)"
   ]
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     "start_time": "2017-09-11T20:42:46.350636"
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   "outputs": [],
   "source": [
    "pois = Poisson(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
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    {
     "data": {
      "text/plain": [
       "0.01831563888873418"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "pois.prob_exactly(0, 2)"
   ]
  },
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   "cell_type": "code",
   "execution_count": 4,
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       "0.9826487347633355"
      ]
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     "execution_count": 4,
     "metadata": {},
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   ],
   "source": [
    "pois.prob_at_least(2, 3)"
   ]
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   "source": [
    "比如，我一个demand，期望每天12个order，假设是泊松分布，可能比12个多可能少；\n",
    "假设supply这边也是泊松分布。\n",
    "\n",
    "那我这个supply的期望需要到多少，才能满足90%的order，这个怎么算？\n",
    "满足度从90%提升到99%，付出的代价肯定是越来越高的，所以不追求一定要满足所有order。\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\"满足\"是指在一段时间（比如一年）的总体供应量大于总需求的90%吗？\n",
    "还是说只讨论\"当天供应\"对\"当天需求\"，有90%的天数是供应完全覆盖了需求的？\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "我的目标是，一段时间内比如一年，90%的order能在当天被满足。\n",
    "当天匹配不上就失效了。然后再算算99%能在当天满足的情况。\n",
    "然后比比做这个改进需要付出多大成本。不是指90%的天数，指order数量的90%"
   ]
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   "outputs": [],
   "source": [
    "pois = Poisson(rate=12)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
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    {
     "data": {
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       "0.5384026669363818"
      ]
     },
     "execution_count": 11,
     "metadata": {},
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   ],
   "source": [
    "pois.prob_at_least(12, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
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     "end_time": "2017-09-11T20:57:14.324589",
     "start_time": "2017-09-11T20:57:14.309544"
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    "collapsed": true
   },
   "outputs": [],
   "source": [
    "probas_exactly = [pois.prob_exactly(n, 1) for n in range(0, 50)]\n",
    "probas_at_least = [pois.prob_at_least(n, 1) for n in range(0, 50)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
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   "outputs": [
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     "name": "stdout",
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     "text": [
      "pois = Poisson(rate=12)\n",
      "\n",
      "\n",
      "出现精确n次事件的概率 (t=1天)\n"
     ]
    },
    {
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9LGsFRltrEwDGmDrgD8DXB9pIfX0NrhsuuPBCNDTU+fp5w+6PtwJQ++8fp7bI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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a788c57860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "\n",
      "至少出现n次事件的概率 (t=1天)\n"
     ]
    },
    {
     "data": {
      "image/png": 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d6v2M4G3QKit33fuqq/via4YP/+Jr6uq8n6WtfdiwXdvfeWf37R29ZsiQXZex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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a788c96fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print('pois = Poisson(rate=12)')\n",
    "\n",
    "fig = plt.figure(figsize = (8, 4))\n",
    "print('\\n\\n出现精确n次事件的概率 (t=1天)')\n",
    "plt.plot(probas_exactly, 'r.-')\n",
    "plt.show()\n",
    "\n",
    "fig = plt.figure(figsize = (8, 4))\n",
    "print('\\n\\n至少出现n次事件的概率 (t=1天)')\n",
    "plt.plot(probas_at_least, 'b.-')\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": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}