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{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#  Histogrammes "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Graphiques en batons"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x= [1,1.5,2,2.5,3]\n",
    "y= [1,4,3,4,1]\n",
    "\n",
    "\"\"\" Par défaut  width=0.8, ce qui ne ferait pas joli ici\"\"\"\n",
    "plt.bar(x,y,edgecolor=\"k\",width=0.5); # \"k\" c'est black\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\"\"\" Population totale par sexe et âge au 1er janvier 2018, France. source:\n",
    "https://www.insee.fr/fr/statistiques/fichier/1892086/pop-totale-france.xls \"\"\"\n",
    "nb_hommes=[370264,380786,390091,398757,409096,419458,422341,433633,433293,435936,432382,439050,429300,427923,426042,428943,436599,442760,420335,411745,397771,394287,384071,365958,361467,378875,380348,386998,386152,391032,392666,397890,400708,396839,392953,417916,422120,429147,406565,399665,406674,394569,405691,428904,452528,462957,459928,451838,443890,438042,436591,445267,446241,448156,443106,425952,424946,421198,414831,404537,400466,395119,387700,385660,374649,378923,368702,381299,370877,367734,357172,334517,249885,240416,230819,211303,184231,186016,189134,179799,169183,162468,149256,142187,126683,119777,106150,94411,76897,65760,54174,43318,35138,26429,19424,14138,10396,7400,2994,1612,2929,]\n",
    "nb_femmes=[354226,363749,373574,386477,389867,398597,405611,415679,412153,415631,413237,420649,411513,409866,407270,408649,416111,421402,398604,394150,380429,381718,374299,363324,360271,378034,385787,396563,401533,408101,410675,420196,419362,418329,413567,437539,440858,446720,423369,413791,414315,405569,414926,435625,461600,470512,467329,459041,453968,453315,449798,459334,459223,465447,461150,445813,446626,446154,444025,434265,433063,429825,425865,424456,416053,420938,410389,425522,417056,411404,404106,382498,289497,281703,273366,251816,224905,234778,243629,239419,233198,231156,222866,220997,205946,204422,188772,178310,153484,139112,120327,105685,90293,73890,60007,48181,36624,27518,11907,7042,13945,]\n",
    "nb_femmes=-np.array(nb_femmes)\n",
    "\n",
    "ages=range(0,len(nb_hommes))\n",
    "\n",
    "\n",
    "plt.bar(ages,nb_hommes,width=1,label=\"hommes\")\n",
    "plt.bar(ages,nb_femmes,width=1,label=\"femmes\")\n",
    "xticks=np.arange(0,101,10)\n",
    "plt.xticks(xticks)\n",
    "for x in xticks: plt.axvline(x,color=\"0.9\",linewidth=0.3)\n",
    "plt.legend();\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***Exo:*** changez les abscisses pour faire apparaitre les années de naissances. Essayez de justifier les trous et les renflements dans la pyramide des âges. \n",
    "\n",
    "***Exo:*** Expliquez l'anomalie à l'extrémité droite de la pyramide des âges. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Histogrammes\n",
    "\n",
    "\n",
    "\n",
    "Considérons maintenant un échantillon c.à.d un ensemble de nombre. Dans la plupart des cas les échantillons sont construit:\n",
    "\n",
    "* soit à partir de simulation successive de v.a (ex: v.a gaussienne)\n",
    "* soit à partir d'observations (ex: tailles des gens dans la rue)\n",
    "\n",
    "Dresser l'histogramme d'un échantillon consiste à découper les réel en sous-interavalles, puis d'afficher des batons qui ont pour base ces sous-intervallse, et comme hauteur le nombre d'élément de l'échantillon contenu dans chaque sous-intervalles. \n",
    "\n",
    "\n",
    "### Découpage automatique\n",
    "\n",
    "Ci-dessous, `bins=n` signigie que l'on découpe l'intervalle `[min(X),max(X)]` en n sous-intervalles."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\"\"\"l'échantillon à observer\"\"\"\n",
    "X=np.random.normal(0,1,size=1000)\n",
    "plt.hist(X,bins=15,edgecolor=\"k\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Récupérer les valeurs numériques\n",
    "\n",
    "Les fonctions `plt.hist()` et `np.histogram()` (idem mais sans affichage) permettent aussi de récupérer des valeurs numériques."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "hauteur des batons\n",
      " [ 36. 253. 450. 232.  29.]\n",
      "découpage\n",
      " [-3.03749776 -1.79027834 -0.54305892  0.7041605   1.95137992  3.19859934]\n",
      "hauteur des batons\n",
      " [ 36 253 450 232  29]\n",
      "découpage\n",
      " [-3.03749776 -1.79027834 -0.54305892  0.7041605   1.95137992  3.19859934]\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a=plt.hist(X,bins=5,edgecolor=\"k\")\n",
    "print(\"hauteur des batons\\n\",a[0])\n",
    "print(\"découpage\\n\",a[1])\n",
    "b=np.histogram(X,bins=5)\n",
    "print(\"hauteur des batons\\n\",b[0])\n",
    "print(\"découpage\\n\",b[1])    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Découpage à la main\n",
    "\n",
    "Mais parfois il est préférable de préciser nous même les sous-intervalles (=la base des batons)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXoAAAD8CAYAAAB5Pm/hAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMi4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvhp/UCwAAEPlJREFUeJzt3X+s3XV9x/HnaxTUqLMg19q0xZLYaIiZwG5YjWZROg0gsWxRotmkY126P3DBaKI4/1hM9odkiSjZwtKIs2xMJSihQaZ2FWNMBlq0olAcV2Jtb1paUfAHUYe+98f9NF66tuec3nt77v3wfCQn5/P5fD/f832fpnnd7/2c7/neVBWSpH793rgLkCQtLINekjpn0EtS5wx6SeqcQS9JnTPoJalzA4M+ySuS7J71+GmSdyc5K8mOJI+05zPb/CS5MclUkgeSXLjwb0OSdDwDg76qvldV51fV+cAfAk8BdwDXATurah2ws/UBLgXWtccW4KaFKFySNJxRl242AN+vqr3ARmBbG98GXNHaG4Fbasa9wPIkK+elWknSyJaNOP/twKdae0VVHWjtg8CK1l4F7Ju1z/42doDjOPvss2vt2rUjliJJz27333//j6pqYtC8oYM+yRnAW4APHL2tqirJSPdSSLKFmaUdzjnnHHbt2jXK7pL0rJdk7zDzRlm6uRT4ZlU91vqPHVmSac+H2vg0sGbWfqvb2DNU1daqmqyqyYmJgT+QJEknaZSgfwe/W7YB2A5sau1NwJ2zxq9qV9+sB56ctcQjSTrFhlq6SfJ84I3A38wa/jBwW5LNwF7gyjZ+N3AZMMXMFTpXz1u1kqSRDRX0VfUL4MVHjT3OzFU4R88t4Jp5qU6SNGd+M1aSOmfQS1LnDHpJ6pxBL0mdM+glqXOj3gJh0Vm5+hwOTu8bPFGLxktXreHA/h+OuwzpWWPJB/3B6X287P13jbsMjWDv9ZePuwTpWcWlG0nqnEEvSZ0z6CWpcwa9JHXOoJekzhn0ktQ5g16SOmfQS1LnDHpJ6pxBL0mdM+glqXMGvSR1zqCXpM4Z9JLUOYNekjo3VNAnWZ7k9iQPJ9mT5DVJzkqyI8kj7fnMNjdJbkwyleSBJBcu7FuQJJ3IsGf0HwO+UFWvBF4N7AGuA3ZW1TpgZ+sDXAqsa48twE3zWrEkaSQDgz7Ji4A/Bm4GqKpfV9UTwEZgW5u2DbiitTcCt9SMe4HlSVbOe+WSpKEMc0Z/LnAY+Nck30ry8STPB1ZU1YE25yCworVXAbP/iOv+NiZJGoNhgn4ZcCFwU1VdAPyC3y3TAFBVBdQoB06yJcmuJLsOHz48yq6SpBEME/T7gf1VdV/r385M8D92ZEmmPR9q26eBNbP2X93GnqGqtlbVZFVNTkxMnGz9kqQBBgZ9VR0E9iV5RRvaADwEbAc2tbFNwJ2tvR24ql19sx54ctYSjyTpFFs25Ly/BW5NcgbwKHA1Mz8kbkuyGdgLXNnm3g1cBkwBT7W5kqQxGSroq2o3MHmMTRuOMbeAa+ZYlyRpnvjNWEnqnEEvSZ0z6CWpcwa9JHXOoJekzhn0ktQ5g16SOmfQS1LnDHpJ6pxBL0mdM+glqXMGvSR1zqCXpM4Z9JLUOYNekjpn0EtS5wx6SeqcQS9JnTPoJalzBr0kdc6gl6TOGfSS1Lmhgj7JD5J8J8nuJLva2FlJdiR5pD2f2caT5MYkU0keSHLhQr4BSdKJjXJG/4aqOr+qJlv/OmBnVa0DdrY+wKXAuvbYAtw0X8VKkkY3l6WbjcC21t4GXDFr/JaacS+wPMnKORxHkjQHwwZ9AV9Kcn+SLW1sRVUdaO2DwIrWXgXsm7Xv/jYmSRqDZUPOe11VTSd5CbAjycOzN1ZVJalRDtx+YGwBOOecc0bZVZI0gqHO6Ktquj0fAu4ALgIeO7Ik054PtenTwJpZu69uY0e/5taqmqyqyYmJiZN/B5KkExoY9Emen+SFR9rAm4DvAtuBTW3aJuDO1t4OXNWuvlkPPDlriUeSdIoNs3SzArgjyZH5/1FVX0jyDeC2JJuBvcCVbf7dwGXAFPAUcPW8Vy1JGtrAoK+qR4FXH2P8cWDDMcYLuGZeqpMkzZnfjJWkzhn0ktQ5g16SOmfQS1LnDHpJ6pxBL0mdM+glqXMGvSR1zqCXpM4Z9JLUOYNekjpn0EtS5wx6SeqcQS9JnTPoJalzBr0kdc6gl6TOGfSS1DmDXpI6Z9BLUucMeknqnEEvSZ0bOuiTnJbkW0nuav1zk9yXZCrJZ5Kc0caf0/pTbfvahSldkjSMUc7orwX2zOpfD9xQVS8HfgJsbuObgZ+08RvaPEnSmAwV9ElWA28GPt76AS4Gbm9TtgFXtPbG1qdt39DmS5LGYNgz+o8C7wN+2/ovBp6oqqdbfz+wqrVXAfsA2vYn23xJ0hgMDPoklwOHqur++Txwki1JdiXZdfjw4fl8aUnSLMOc0b8WeEuSHwCfZmbJ5mPA8iTL2pzVwHRrTwNrANr2FwGPH/2iVbW1qiaranJiYmJOb0KSdHwDg76qPlBVq6tqLfB24MtV9efAPcBb27RNwJ2tvb31adu/XFU1r1VLkoY2l+vo3w+8J8kUM2vwN7fxm4EXt/H3ANfNrURJ0lwsGzzld6rqK8BXWvtR4KJjzPkl8LZ5qE2SNA/8Zqwkdc6gl6TOGfSS1DmDXpI6Z9BLUucMeknqnEEvSZ0z6CWpcwa9JHXOoJekzhn0ktQ5g16SOmfQS1LnDHpJ6pxBL0mdM+glqXMGvSR1zqCXpM4Z9JLUOYNekjpn0EtS5wx6SercwKBP8twkX0/y7SQPJvlQGz83yX1JppJ8JskZbfw5rT/Vtq9d2LcgSTqRYc7ofwVcXFWvBs4HLkmyHrgeuKGqXg78BNjc5m8GftLGb2jzJEljMjDoa8bPW/f09ijgYuD2Nr4NuKK1N7Y+bfuGJJm3iiVJIxlqjT7JaUl2A4eAHcD3gSeq6uk2ZT+wqrVXAfsA2vYngRfPZ9GSpOENFfRV9ZuqOh9YDVwEvHKuB06yJcmuJLsOHz4815eTJB3HSFfdVNUTwD3Aa4DlSZa1TauB6daeBtYAtO0vAh4/xmttrarJqpqcmJg4yfIlSYMMc9XNRJLlrf084I3AHmYC/61t2ibgztbe3vq07V+uqprPoiVJw1s2eAorgW1JTmPmB8NtVXVXkoeATyf5B+BbwM1t/s3AvyWZAn4MvH0B6pYkDWlg0FfVA8AFxxh/lJn1+qPHfwm8bV6qkyTNmd+MlaTOGfSS1DmDXpI6Z9BLUucMeknqnEEvSZ0z6CWpcwa9JHXOoJekzhn0ktQ5g16SOmfQS1LnDHpJ6pxBL0mdM+glqXMGvSR1zqCXpM4Z9JLUOYNekjpn0EtS5wx6SeqcQS9JnRsY9EnWJLknyUNJHkxybRs/K8mOJI+05zPbeJLcmGQqyQNJLlzoNyFJOr5hzuifBt5bVecB64FrkpwHXAfsrKp1wM7WB7gUWNceW4Cb5r1qSdLQBgZ9VR2oqm+29s+APcAqYCOwrU3bBlzR2huBW2rGvcDyJCvnvXJJ0lBGWqNPsha4ALgPWFFVB9qmg8CK1l4F7Ju12/42Jkkag6GDPskLgM8C766qn87eVlUF1CgHTrIlya4kuw4fPjzKrpKkEQwV9ElOZybkb62qz7Xhx44sybTnQ218Glgza/fVbewZqmprVU1W1eTExMTJ1i9JGmCYq24C3AzsqaqPzNq0HdjU2puAO2eNX9WuvlkPPDlriUeSdIotG2LOa4F3At9JsruN/R3wYeC2JJuBvcCVbdvdwGXAFPAUcPW8VixJGsnAoK+qrwE5zuYNx5hfwDVzrEuSNE/8Zqwkdc6gl6TOGfSS1DmDXpI6Z9BLUucMeknqnEEvSZ0z6CWpc8N8M1ZaElauPoeD0/sGT5QWkZeuWsOB/T9c0GMY9OrGwel9vOz9d427DGkke6+/fMGP4dKNJHXOM3qdeqedzsxNUSWdCga9Tr3f/O+CLLGcil+BpaXIpRtJ6pxBL0mdM+glqXMGvSR1zqCXpM4Z9JLUOYNekjpn0EtS5wx6SercwKBP8okkh5J8d9bYWUl2JHmkPZ/ZxpPkxiRTSR5IcuFCFi9JGmyYM/pPApccNXYdsLOq1gE7Wx/gUmBde2wBbpqfMiVJJ2tg0FfVV4EfHzW8EdjW2tuAK2aN31Iz7gWWJ1k5X8VKkkZ3smv0K6rqQGsfBFa09ipg9l9+2N/GJEljMucPY6uqgBp1vyRbkuxKsuvw4cNzLUOSdBwnG/SPHVmSac+H2vg0sGbWvNVt7P+pqq1VNVlVkxMTEydZhiRpkJMN+u3AptbeBNw5a/yqdvXNeuDJWUs8kqQxGPiHR5J8Cng9cHaS/cDfAx8GbkuyGdgLXNmm3w1cBkwBTwFXL0DNkqQRDAz6qnrHcTZtOMbcAq6Za1GSpPnjN2MlqXMGvSR1zqCXpM4Z9JLUOYNekjpn0EtS5wx6SeqcQS9JnTPoJalzBr0kdc6gl6TOGfSS1DmDXpI6Z9BLUucMeknqnEEvSZ0z6CWpcwa9JHXOoJekzhn0ktQ5g16SOmfQS1LnFiTok1yS5HtJppJctxDHkCQNZ96DPslpwD8DlwLnAe9Ict58H0eSNJyFOKO/CJiqqker6tfAp4GNC3AcSdIQFiLoVwH7ZvX3tzFJ0hikqub3BZO3ApdU1V+3/juBP6qqdx01bwuwpXVfAXzvJA95NvCjk9x3HJZSvUupVlha9S6lWmFp1buUaoW51fuyqpoYNGnZSb74iUwDa2b1V7exZ6iqrcDWuR4sya6qmpzr65wqS6nepVQrLK16l1KtsLTqXUq1wqmpdyGWbr4BrEtybpIzgLcD2xfgOJKkIcz7GX1VPZ3kXcAXgdOAT1TVg/N9HEnScBZi6Yaquhu4eyFe+xjmvPxzii2lepdSrbC06l1KtcLSqncp1QqnoN55/zBWkrS4eAsESepcF0Gf5B+TPJzkgSR3JFk+7ppOJMnbkjyY5LdJFuXVAUvpNhZJPpHkUJLvjruWQZKsSXJPkofa/4Frx13T8SR5bpKvJ/l2q/VD465pkCSnJflWkrvGXcsgSX6Q5DtJdifZtZDH6iLogR3Aq6rqD4D/AT4w5noG+S7wZ8BXx13IsSzB21h8Erhk3EUM6WngvVV1HrAeuGYR/9v+Cri4ql4NnA9ckmT9mGsa5Fpgz7iLGMEbqur8pXh55SlXVV+qqqdb915mrt1ftKpqT1Wd7BfEToUldRuLqvoq8ONx1zGMqjpQVd9s7Z8xE0qL8pvjNePnrXt6eyzaD/WSrAbeDHx83LUsNl0E/VH+CvjPcRexxHkbi1MgyVrgAuC+8VZyfG0pZDdwCNhRVYu2VuCjwPuA3467kCEV8KUk97c7BSyYBbm8ciEk+S/gpcfY9MGqurPN+SAzvxrfeiprO5Zh6tWzV5IXAJ8F3l1VPx13PcdTVb8Bzm+fe92R5FVVteg+C0lyOXCoqu5P8vpx1zOk11XVdJKXADuSPNx+O513Syboq+pPTrQ9yV8ClwMbahFcMzqo3kVuqNtY6OQkOZ2ZkL+1qj437nqGUVVPJLmHmc9CFl3QA68F3pLkMuC5wO8n+feq+osx13VcVTXdng8luYOZJdMFCfoulm6SXMLMr2xvqaqnxl1PB7yNxQJJEuBmYE9VfWTc9ZxIkokjV7AleR7wRuDh8VZ1bFX1gapaXVVrmfn/+uXFHPJJnp/khUfawJtYwB+gXQQ98E/AC5n59Wd3kn8Zd0EnkuRPk+wHXgN8PskXx13TbO2D7SO3sdgD3LaYb2OR5FPAfwOvSLI/yeZx13QCrwXeCVzc/q/ubmehi9FK4J4kDzDzw39HVS36yxaXiBXA15J8G/g68Pmq+sJCHcxvxkpS53o5o5ckHYdBL0mdM+glqXMGvSR1zqCXpM4Z9JLUOYNekjpn0EtS5/4PvqmTos8s5l4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X=np.random.normal(0,1,size=1000)\n",
    "plt.hist(X, bins=[-2,0.5,1,5],edgecolor=\"k\"); #un choix particulièrement idiot de bins"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Histogramme de loi discrète"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Attention, pour les lois discrètes il faut obligatoirement préciser le découpage.\n",
    "Pour voir une catastrophe, essayez `bins=11` dans l'histrogramme ci-dessous. Expliquez le phénomène."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n=10\n",
    "X=np.random.binomial(n,0.5,size=3000)\n",
    "\n",
    "\"\"\"attention np.arange(0,n+2,1) donne l'intervalle discret [0,n+2[= [0,n+1].\n",
    " on lui soustrait ensuite 0.5 pour avoir chaque entier de [0,n] dans un sous-intervalle\"\"\"\n",
    "bins=np.arange(0,n+2,1)-0.5\n",
    "\n",
    "plt.hist(X,bins=bins,edgecolor=\"k\") \n",
    "\"\"\"on précise les graduations en x\"\"\"\n",
    "plt.xticks(np.arange(0,n+1,1));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "En fait, pour les histogrammes de loi discrète, il est plus simple de ne pas utiliser `plt.hist()`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10]), array([  5,  30, 134, 385, 664, 692, 580, 363, 113,  31,   3]))\n"
     ]
    },
    {
     "data": {
      "image/png": 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+qb+WIclnkhxL8tQS1FqX5KEkzyR5OslHlqDm65L8VZKvt5q/P3TNVveCJI8n+fIS1Nqf5BtJnkgyuwT1Via5J8k3k+xN8o4Ba13ZXtfxx/eSfHSoevPq/kb7+/JUkruTvG7geh9ptZ4e4vWd7Oc8yaVJHkzybNteMum6i1ZV3T8YvSn8beAngYuArwNXDVzzXcC1wFNL8PpWA9e29puAv1mC1xfgja19IfAIcP0SvNaPAZ8DvrwEtfYDlw9dZ169ncCvtvZFwMolqnsBcJTRPdlD1lkD/C3w+ra/C/iVAeu9FXgKeAOj9yP/FHjLhGv8u59z4H8AW1t7K/Dxpfo7dKrH+XJF//+/lqGqfgAc/1qGwVTVXwDfHbLGvFpHquqx1v5HYC+jH6oha1ZV/VPbvbA9Bn3DJ8la4Gbg00PWWQ5J3swoNHYAVNUPqurFJSq/Afh2VR1YglorgNcnWcEogP9+wFo/DTxSVS9X1SvAnwO/MMkCp/g538joH23a9pZJ1jwT50vQn+xrGQYNwuWSZBq4htEV9tC1LkjyBHAMeLCqhq75h8BvAf82cJ3jCvhqkkfbJ7mHdAUwB/xRW5r6dJKLB6553G3A3UMXqarDwP8E/g44ArxUVV8dsORTwH9JclmSNwA38eoPcw5lVVUdae2jwKolqHla50vQnxeSvBH4IvDRqvre0PWq6odVdTWjTz9fl+StQ9VK8l7gWFU9OlSNk/jZqrqW0Tex3pHkXQPWWsFoCeDOqroG+D6j//YPqn2o8X3AHy9BrUsYXe1eAfwH4OIkvzxUvaraC3wc+CrwFeAJ4IdD1TvFHIqB/6c7jvMl6Mf6WobXsiQXMgr5z1bVl5aydltieAi4YcAy7wTel2Q/o6W3dyf5vwPWO34FSlUdA+5ltAQ4lEPAoXn/K7qHUfAP7Ubgsap6fglq/Tfgb6tqrqr+FfgS8J+HLFhVO6rqZ6rqXcALjN6/GtrzSVYDtO2xJah5WudL0Hf9tQxJwmhtd29V/cES1ZxKsrK1Xw+8B/jmUPWq6neqam1VTTP68/taVQ12NZjk4iRvOt4Gfp7RUsAgquoocDDJla1rAwN9tfcJPsASLNs0fwdcn+QN7e/sBkbvJw0myU+07X9ktD7/uSHrNbuBTa29CbhvCWqe1iCfjD3X1DJ8LUOSu4GfAy5Pcgj4varaMVC5dwIfBL7R1swBfrdGn1AeympgZ/tFMz8G7KqqwW95XEKrgHtHecQK4HNV9ZWBa/468Nl2MfIccPuQxdo/YO8Bfm3IOsdV1SNJ7gEeA14BHmf4T5F+McllwL8Cd0z6De6T/ZwD24BdSTYDB4BbJ1nzTPjJWEnq3PmydCNJ5y2DXpI6Z9BLUucMeknqnEEvSZ0z6CWpcwa9JHXOoJekzv0/GSffXwnrw2oAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "freq=np.unique(X,return_counts=True)\n",
    "print(freq)\n",
    "plt.bar(freq[0],freq[1])\n",
    "plt.xticks(freq[0]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***A vous:***  Pourquoi $(1\\heartsuit)$ la précédure numpy qui compte les occurence d'appelle `np.unique()`? "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Entre discret et continue. \n",
    "\n",
    "Quand une loi discréte a un support très très grand exemple $[0,...,15000]$, on peut faire comme si c'était une loi continue: En divisant ce support en une vingtaine de sous-intervalle, chacun d'entre eux occupera grosso modo le même nombre d'entier. Mais il y a des cas intermédiare comme ci-dessous, où  il faut regrouper proprement les entiers. \n",
    "\n",
    "***A vous:*** Améliorer $(2\\heartsuit)$  l'histogramme ci-dessous. Aide: deux solutions:\n",
    "\n",
    "* soit utiliser `plt.hist()` en faisant des bins à la main\n",
    "* soit utiliser `np.unique()` et `plt.bar()` en quantizant (=en regroupant les valeur) avec la division entière `//`. \n",
    "\n",
    "Question subsidière $(4\\diamondsuit)$: Montrez qu'une telle loi géomètrique, c'est quasiment une loi exponentielle. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<BarContainer object of 797 artists>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X=np.random.geometric(0.001,size=1000)\n",
    "freq=np.unique(X,return_counts=True)\n",
    "plt.bar(freq[0],freq[1]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plusieurs histogrammes\n",
    "\n",
    "Comparons des lois béta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nbData=10000\n",
    "X1=np.random.beta(3,1,size=nbData)\n",
    "X2=np.random.beta(2,3,size=nbData)\n",
    "X3=np.random.beta(1,0.5,size=nbData)\n",
    "\n",
    "plt.hist([X1,X2,X3],bins=20,label=[\"a=3,b=1\",\"a=2,b=3\",\"a=1,b=0.5\"]);\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La variété des formes possible d'une loi la rend très pratique en modélisation. Choisissez des lois bêta bien choisies (dilatée par une constante), pour modéliser les variables X suivantes:\n",
    "\n",
    " * X : quantité chocolat consommée par les français  (sachant que plus on en mange, et plus on a envie d'en manger)\n",
    " * X : durée de vie des français \n",
    " * X : durée de vie des grenouilles (forte mortalité infantile)\n",
    " \n",
    "Dressez les histogrammes. Connaissez-vous d'autre loi pour des durées de vie ?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\"\"\" on peut aussi superposer les histogrammes en utilisant la transparence (alpha=0.5),\n",
    "mais au-dela de 2 histogrammes cela devient confus\"\"\"\n",
    "plt.hist(X1,bins=20,label=\"a=3,b=1\")\n",
    "plt.hist(X2,bins=20,label=\"a=2,b=3\",alpha=0.5);\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Superposons histogramme et densité "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### La gaussienne\n",
    "\n",
    "L'option importante pour que l'histogramme se superpose à une densité c'est `density=True`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nbSimu=1000\n",
    "Simu=np.random.normal(size=nbSimu)\n",
    "\n",
    "\"\"\"formule à emmener partout avec soi\"\"\"\n",
    "def gaussian_density(x):\n",
    "    return 1/(np.sqrt(2*np.pi))*np.exp(-0.5*x**2)\n",
    "\n",
    "plt.hist(Simu,bins=30,density=True,edgecolor=\"k\");\n",
    "\n",
    "x=np.linspace(-3,3,200)\n",
    "plt.plot(x, gaussian_density(x));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Tronquer un histogramme\n",
    "\n",
    "Parfois on a envit de ne montrer qu'une partie de l'histogramme. `plt.hist()` dispose d'une option `range` qui ignore les valeurs de l'échantillon en dehors du range. Mais malheureusement, `plt.hist()` utlise la normalisation 'naturelle' qui n'est pas compatible avec la superposition avec la densité théorique.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X=np.random.normal(0,1,size=1000)\n",
    "plt.hist(X,bins=15,range=[0,5],density=True,edgecolor=\"k\");\n",
    "x=np.linspace(0,5,200)\n",
    "plt.plot(x, gaussian_density(x));\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Il faut donc faire la normalisation à la main, en précisant le poids de chaque observation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X=np.random.normal(0,1,size=1000)\n",
    "\n",
    "nb_batons=30\n",
    "gauche=0\n",
    "droite=5\n",
    "bins=np.linspace(gauche,droite,nb_batons)\n",
    "step=(droite-gauche)/nb_batons\n",
    "\"\"\"Ici une formule à connaitre par coeur (ce qui ne dispense pas de la comprendre)\"\"\"\n",
    "weights=np.ones_like(X)/step/len(X)\n",
    "\n",
    "plt.hist(X,bins=bins,weights=weights,range=[gauche,droite],edgecolor=\"k\")\n",
    "x=np.linspace(gauche,droite,200)\n",
    "plt.plot(x, gaussian_density(x));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### La Cauchy\n",
    "\n",
    "***Exo:*** Ci-dessous un histogramme très laid d'un échantillon de loi de Cauchy.  Améliorez! \n",
    "\n",
    "**Aide:** Plutôt que de recopier le code précédent, créez une petite fonction qui trace un histogramme tronqué. Elle pourrait par exemple avoir comme signature : `hist_tronc(ech,gauche,droite,nb_batons)`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "def cauchy_density(x):\n",
    "    return 1/np.pi/(1+x**2)\n",
    "\n",
    "\n",
    "X=np.random.standard_cauchy(size=200)\n",
    "plt.hist(X,bins=15,density=True,edgecolor=\"k\");\n",
    "x=np.linspace(-10,10,200)\n",
    "plt.plot(x, cauchy_density(x));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###  Une loi log-normale\n",
    " \n",
    "***Exo:*** Que représente une distribution log-normale ? Réponse : c'est la distribution de $f(X)$ avec $f$ ... et $X$ ... Vérifiez votre réponse en superposant histogramme de $f(X)$  à l'histogramme proposé ci-dessous. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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xPENVVQ8kOQx8mblPhD1Eg1eqJvks8HbgoiQzwO8BtwH3JrkeeBz45aHs2ytUJak9a+20jCSpA+MuSQ0y7pLUIOMuSQ0y7pLUIOMuSQ0y7pLUIOMuSQ36f/07m3HKeg9UAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "size=1000\n",
    "X=np.random.lognormal(size=size)\n",
    "bins=np.linspace(0,10,20)\n",
    "plt.hist(X, bins=bins, density=True,edgecolor=\"k\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***Exo suite:***  Réponse de la première partie : la loi log-normale c'est la loi de $\\exp(X)$ avec $X \\sim Normale(0,1)$. A partir de cette description, vous devriez pouvoir intuitivement comprendre que la densité de la log-normale en 0 vaut ... Ce fait est très mal illustrer par l'histrogramme ci-dessus. Modifiez-le ! \n",
    "\n",
    "\n",
    "\n",
    "***Exo fin:*** Complétez le calcul de la densité de la log-normale: Considérons $\\phi$ une fonction teste et $X$ une v.a de loi normale.\n",
    "$$\n",
    "     \\mathbf   E [\\phi( \\exp(X) )] =  cst  \\int \\ \\phi( e^x ) \\  e^{- \\frac {1}{2} x^2 }\\ dx \n",
    "$$\n",
    "on fait le changement de variable $e^x \\to  y$ on trouve ... donc la densité de $\\exp(X)$ est ...\n",
    "\n",
    "Superposez cette densité avec l'histogramme précédent pour valider votre calcul.\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Une loi binomiale\n",
    "\n",
    "Quelle est le lien entre loi binomiale et loi de bernouilli ?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X: [3 2 4 8 3 7 7 7 5 5 3 7 4 6 4 6 7 4 5 5 6 3 6 5 3 4 7 5 6 6 6 6 7 5 4 4 2 5 5 4 4 4 4 6 3 5 6 7 5 5 3 8 5 4 6 6 5 5 3 5 4 6 7 8 4 5 5 6 3 6 5 3 5 6 7 4 6 4 6 4 8 4 6 4 8 5 5 5 3 5 2 4 6 4 5 6 6 4 4 5]\n"
     ]
    }
   ],
   "source": [
    "\"\"\" échantillon d'une binomiale \"\"\"\n",
    "X=np.random.binomial(n=10,p=0.5,size=100)\n",
    "np.set_printoptions(linewidth=2000)\n",
    "print(\"X:\",X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Dressez l'histogramme de ces simulations. Superposez cet histogramme avec la densité discrète de la loi binomiale. \n",
    "\n",
    "On calculera cette densité point par point (sans chercher de package particulier). Vous aurez seulement besoin de la fonction factorielle dispobible dans le package `math`.\n",
    "\n",
    "Remarque : Il est plus élégant de ne pas relier les points d'une densité discrète. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10!: 3628800\n"
     ]
    }
   ],
   "source": [
    "import math\n",
    "print(\"10!:\",math.factorial(10))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Histogramme 2D\n",
    "\n",
    "Analysez le programme suivant.\n",
    "\n",
    "* Remplacez les commentaires-questions par de vrais commentaires de programme.\n",
    "* Quel est l'intérêt de la fonction `test()`\n",
    "* Que se passe-t-il si on change `T=100` en `T=200` ? \n",
    "* Pourquoi l'histogramme final a-t-il un aspect de quadriallage? Aide: c'est mathématique, ce n'est pas un artefact de l'affichage. \n",
    "* Si l'on lise ce quadriallage,  à quoi ressemble cet histogramme? En vertu de quel théorème?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [],
   "source": [
    "def makeTrajectories(T,nbSimu):\n",
    "    pre_pas=np.random.randint(0, 4, size=[nbSimu,T])\n",
    "    pas=np.zeros(shape=[nbSimu,T, 2])\n",
    "    \"\"\"Qu'est-ce que qu'on fait ici?\"\"\"\n",
    "    pas[pre_pas==0]=[2,1]\n",
    "    pas[pre_pas==1]=[-1,0]\n",
    "    pas[pre_pas==2]=[0,1]\n",
    "    pas[pre_pas==3]=[0,-1]\n",
    "    \"\"\"C'est quoi cumsum, pourquoi  axis=1?\"\"\"\n",
    "    return np.cumsum(pas,axis=1)\n",
    "\n",
    "\n",
    "def test():\n",
    "    trajectories=makeTrajectories(T=7,nbSimu=3)\n",
    "    print(trajectories.shape)\n",
    "    print(trajectories)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "trajectories=makeTrajectories(T=100,nbSimu=20)\n",
    "for tr in trajectories:\n",
    "    plt.plot(tr[:,0],tr[:,1])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "gauche=-10\n",
    "droite=100\n",
    "\n",
    "trajectories=makeTrajectories(T=100,nbSimu=10000)\n",
    "\"\"\"C'est quoi ce -1?\"\"\"\n",
    "arrivals=trajectories[:,-1,:]\n",
    "bins=np.arange(gauche,droite+1,1,dtype=np.float32)\n",
    "\"\"\"Quels sont les 3 arguments de sortie\"\"\"\n",
    "fig,ax=plt.subplots()\n",
    "fig.set_size_inches(5,5)\n",
    "ax.set_aspect(\"equal\")\n",
    "ax.hist2d(arrivals[:,0],arrivals[:,1],bins=[bins,bins],cmap=\"jet\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Résumé fonctionnel"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Les arguments important de `plt.hist()`:\n",
    "\n",
    "L'argument obligatoire:\n",
    "\n",
    "* `x:` les données \n",
    "\n",
    "\n",
    "Argument sur le traitement des données :\n",
    "\n",
    "* `bins`: découpage en sous-intervalles. Soit un nombre, soit une liste.  \n",
    "* `density=True`: la hauteur des batons est normalisée pour que cela ressemble à une densité\n",
    "* `range=[gauche,droite]`: les données sont limitées à l'intervale donnée. Attention, l'option `density=True` donne dans ce cas un résultat bizarre. Il faut donc utiliser l'option suivante. \n",
    "* `weights`: pondère les données. Pour superposer avec la densité `weights=np.ones_like(X)/step/len(X)` où `step` est la largeur de chaque sous-intervalle. \n",
    "\n",
    "Options de présentation\n",
    "\n",
    "* `orientation:` `\"horizontal\"` ou  `\"vertical\"`\n",
    "* `rwidth`: largeur des batons. Ex: `rwidth=0.5`, ils occupent la moitier des sous-intervalles. \n",
    "* `edgecolor`: couleur du pourtour des batons. `\"k\"` pour black, `\"red\"` pour red etc. \n",
    "* `color`: couleur des batons. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X=np.random.normal(size=100)\n",
    "plt.hist(X,bins=10,color=\"red\", density=True,rwidth=0.8,orientation=\"horizontal\",edgecolor=\"k\");"
   ]
  }
 ],
 "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
}