{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Chapter 2 examples.ipynb",
      "provenance": [],
      "collapsed_sections": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "RqEWo16f6mI2"
      },
      "source": [
        "# Example p. 27"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kxMbprk5-cT7"
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from scipy.stats import t, norm, gamma"
      ],
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "T_W8bh8T6nGC"
      },
      "source": [
        "xi = 0.005\n",
        "sigma = 0.05\n",
        "k = 5000\n",
        "\n",
        "x_bar_star = np.zeros(k)\n",
        "s_star = np.zeros(k)\n",
        "s_x_bar = np.zeros(k)\n",
        "s_s_star = np.zeros(k)"
      ],
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8HmPh2vd-pQr"
      },
      "source": [
        "for i in range(k):\n",
        "   x = np.random.normal(size=i+1, loc=xi, scale=sigma)\n",
        "   x_bar_star[i] = np.mean(x)\n",
        "   s_star[i] = np.std(x)"
      ],
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "id": "kuwl5pEZ-I0e",
        "outputId": "1b1edec9-d297-4eac-b3b0-b64013572138"
      },
      "source": [
        "ymin = min(min(x_bar_star), s_star[-1])\n",
        "ymax = max(max(x_bar_star), s_star[-1])\n",
        "\n",
        "plt.plot(x_bar_star)\n",
        "plt.xlabel('Number of simulations')\n",
        "plt.title('Estimated mean')\n",
        "plt.show()\n"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8SfKow801gCF",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "10a11f02-b516-4929-aac5-6a7b781b8452"
      },
      "source": [
        "print(ymin, ymax)"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "-0.02530521513835056 0.05037711486518474\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "id": "ZIQEx2R4-xGU",
        "outputId": "df8e156b-1716-4168-c4e6-0ff4f289a225"
      },
      "source": [
        "plt.plot(s_star, zorder=1)\n",
        "# plt.ylim(ymin, ymax)\n",
        "plt.xlabel('Number of simulations')\n",
        "plt.title('Estimated standard deviation')\n",
        "plt.hlines(y=sigma,xmin=0, xmax=k, zorder=2)\n",
        "plt.show()"
      ],
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "L3d-42TFAaC2"
      },
      "source": [
        "# Example p. 28: Percentiles"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "49NyvnO5AekY"
      },
      "source": [
        "from scipy.stats import t, norm\n",
        "\n",
        "xi = 0.005\n",
        "sigma = 0.05\n",
        "nu = 3\n",
        "yps = [0.95,0.99]\n",
        "\n",
        "q1_star = np.zeros((1000,2))\n",
        "q2_star = np.zeros((1000,2))\n"
      ],
      "execution_count": 8,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6WHrXASUZ4Lk"
      },
      "source": [
        "for i in range(10, 10000,10):\n",
        "  x1 = np.random.normal(size=i, loc=xi, scale=sigma) # normal\n",
        "  x2 = xi+sigma*np.sqrt((nu-2)/nu)*t.rvs(size=i, df=nu) # t\n",
        "  for j in range(2):\n",
        "    q1_star[i//10, j] = sorted(x1)[np.floor(yps[j]*i).astype(np.int64)]\n",
        "    q2_star[i//10, j] = sorted(x2)[np.floor(yps[j]*i).astype(np.int64)]\n"
      ],
      "execution_count": 9,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DpRnHM0kdkLo"
      },
      "source": [
        "# save to file\n",
        "np.savetxt(\"q1_star.csv\", q1_star, delimiter=\",\")\n",
        "np.savetxt(\"q2_star.csv\", q2_star, delimiter=\",\")"
      ],
      "execution_count": 26,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ouAOnrPdggWK"
      },
      "source": [
        "# read from file\n",
        "q1_star = np.genfromtxt('q1_star.csv', delimiter=',')\n",
        "q2_star = np.genfromtxt('q1_star.csv', delimiter=',')"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "id": "JDCG9BOFgt9v",
        "outputId": "5ee6a8f8-297c-4c1f-da83-b61cedd3617a"
      },
      "source": [
        "plt.plot(np.arange(10,10000,10), q1_star[:-1,0], zorder=1)\n",
        "plt.plot(np.arange(10,10000,10), q1_star[:-1,1], zorder=1)\n",
        "plt.xlabel(\"Number of simulations\")\n",
        "plt.ylabel(\"Estimated percentiles\")\n",
        "plt.title(\"Normal distribution\")\n",
        "plt.hlines(norm.ppf(yps[0], loc=xi, scale=sigma), xmin=0, xmax=10000-1, zorder=2)\n",
        "plt.hlines(norm.ppf(yps[1], loc=xi, scale=sigma), xmin=0, xmax=10000-1, zorder=2)\n",
        "plt.show()"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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Ghfa7t3yqfZcFufDmKfDeWaH51s4JhqJ7n33qOzYoZeanVqiWAzqTGijRSe016ZTUIQO8crSdrRwYmQR8BntDUUFQg3Dz93cll0tIityRJ0QZG7x1Khzi+fIW5gcF1bZV9ouet82OYDPr2xDeOh2D+1gEeP9cWDYR+r0eTNvs+ZEH+Pn/oHN//44rgHfEGxBabrPa5qV2bsqqPyLXA7ZdAYe/l0dqwa2/Bzs2LwW5obPcd2+1nXhHpzPJ22Y1lZQqwYUXA3x1K7Q8xR4Pvxky60GLE20IcuA7FhB4m5fBc67dCLv9I3jsFngzPoWO5/v/b8c+YTvAO+bY78T45yKPQgt2hw4cpr4N3W6FGs3988fKhgXB44Vj4aenbGe/0UnP226FvrsdbtbOtgOkhWOh1Sl2ANHnxaCfcPpH9q9tHzj/PRjaD6rUgTMHWx/Fz/+x39sT/mW1QIBJzirMjbrazyW/wpzhsOhnOOeNoJDyBo3MdGlWuVuscHvtBOhyAxxxBfw22G4zPGMY9HkJNvxt8057xwqnwEBz7Sw7QGl+go1idGumF30CrU4OPvtXt9oVpMsRFRCAcUYcdfKW2H+qm2/+GXruve5HQS78p1V0YRIrU9/yT4+2BEdCUmQNIhZ/nte8sGN9sDP+4WFY/Iv9K8yDc96yX2A/AtrIwp+CaW5fg5fPromhcS4CI2n3yOu3l6MLB4gsHMAKnGfbRb6+dSVUdxy7a+fAmEFWu/D6oZZO8C//t8tmPvxW+Mcf8JLLCb9jvQ2zrlQ9tFx+BAfuzg3weAM443lX3t2QnGbNRmCXpq/s1Bfpf/DrC3YJejeLxtl31eQYOPlRux7Z0H5wyzSrJf38H3hgszUJjrwLzn8f6nSwJrU/P4bKNWxn6GbMoNDzgKkowO7N9v13ONcK3uRKNn3lNPsHdn2xnR5tdM5wO9oOrJnW8qSgZv/H+/bPS2DgE/h+b15iB0Du1QkezIJDzoYFP4b/tpdPhnVzrba1fHLQ1ArwTm8461V7vHaOKyTeYejZcNff4WbLD86FI6+BpscGNa5ImnecUAEBxZ1odv5KeLNX6DXvlzbSaDIkz/qyEw4lES1qY+1sO2LyUlTor5FEY/NSWD4peL7gx+BxLOGn096J7T4rppWuXYF7u7WSif8tXR17wtS3IDXDzuNw/7+XjA/NN2Fw9Lq2LofJb4SmfXkjrPdxlkfyg0161QqPsY8H03ZtgqQ6weCDpRPsJldgNZxIeDWer2+znyt/t51vQMNYMt4KB7B+lxHOsjIfXRhaPlpwAYSanSDohJ/xidNen+f2CocA7sHKJ1fA8VHm+QS+1wEf3/LJ8EiN8HyzImhd7/YNHruFQ4CFY0Pv48UvYANg8uv2L4A76GPdX1ClFlSqGl6ujBATx9AwEekFPA8kAq8bY57wXD8WeA7oCFxgjPnUST8U+C+QCRQCg4wxH5d0r5ycHDNlypQ9aueEb99nwPUxLrxXtVG40PBS/4jQuRHxIr3mno0oqjUpG9OXm5otrXlkT5GEvYv2Kqt3Lon+kWgVQaR3UqlqyZpsYkpQq8puAxgb/hsPklJLvx9KrKRlRff5HeykZkDVRowd/Y01U+4BIjLVGOMbPx43J7WIJAKDgVOBdsCFIuLV15cCVwDemMOdwGXGmEOAXsBzIhI/MVmSD8JLtDBXCK43FG8iCYdabUsuV5JwiLQwYNQFA0vxDqs1DU9LSY+9vB+bFkXPEwslCYc4jtR88QqH9Jr2M5qZ0/0dzdteujkFpSVewgH2feGwhx1ymZK7zfY3Xu2zjIiniakzMN8YsxBARD4C+gLFoRzGmMXOtZBfgjHmL9fxShFZC2QD8bHbiDD2ihg7qNbHwrwRMWTcyw4vVqo1hb6DraodUNEfnAHPH7pnneaJDwSX5qjeLDi7+4R/w4+PRC531gPwRf8IF4Vip0f3O+2o9vNrg5cz6sLlX8Hgo/Zi9J5L3N/5Re9b7Wtw57Kr89L/wTf3wPoYRvhdrvI3VyWnB/0SnS4KjV5qc7QNSV40Dg67BH59sfRtPGuINSP5mbtiITXTP1qu1alB3whA8xPDncH7Mld+DG/1inw9KS32UF0vx9weGrE2YBk80TBy/nqH7dl9ohDPMNf6gDswebmTVipEpDOQAizwudZfRKaIyJR169btcUNLZWaLZEtNrKBd33o9Dk2OhhotQtNTqsRW/qjrQ89TM4LH6bWCx0lpcNmXkespadnwOq4InBMHho9oc662JqpYljUva9Kzo+c59Sno/Ry06Fn6vTmOijIXITUTbo5gl3aT1Siy9prs2pLWHWmUnm1t6rO/tJ2v9zsSIOdquGkyNOmOryZYvZndP92N+7sRjeYn+KdXbRR6fkEJkxdLQ7dbgsc3TYYM10i/YQyz4ZsdF3qe1RD6vQHXjoGOFwTT6x0KFw2DnKvg3xvggg9t1NuFjjW83+vwD09Enx/nvm0/63SE22bCHXPhhIGhedIy4bT/RK6jZqvo99kD9ul5ECJSF3gPuNKYcGOsMWaIMSbHGJOTnR3DDz3yjWLP67c8BOz9pj63z46ex4+AIAh8QQLmm8y6sZU/5TEYsNSGR4I19fR9Ga75IRjtAvb5mh0XuZ6RdwWPxTOJrvVp9rPWIfYz4CDPqBusG4IC4tox0Pm62NofK9eNC71HgHMiRIi5qdUWcq50wkfFv55I9HwYjv4H3OZZ/iPwjrJ9ftjXjgke9xgAd/4F1/4QPrnwvHfD2+IWeO3ODH2GSCHPqVVsO674OmievGKEjUq6cSI0PDIYQdSip/1MSbcRPV6uG2c7/tOcqKYLPoTTXNvnXvK5feenPxPenuQ0uMozG/rYu+1ous+LVlOKheP/FTxOy4ILHKexJNrvdsuTQ/Pfuzx4/OAWOPq20OtZDaHDOVD/cDj71WD4d3IlG27b+1lITII2p1lh2rqXraftGVCtMTQ+OrS+K0YEhViXG219d823z161of3tJiQEBehVTjj7kddAfcdVcPIg+34DxPp7LyXxFBArALdO1MBJiwkRyQRGAPcbYyLECVYAkSa9eddsKon254SnJaWFp8VCYMSfmAw3ToArnTjpWFTOzAbW/JCWBZ2ckVHjo+0Ocw1yQsMrA534oTHsPtf52tDz7Nb2B3DNaHt+2KXQ4x64ZSqc/Roc7pjGAh1d1UZw2lOhdVzzgzWfXDHSdjIlcZ5r4tmlX9jRXXVnZO3WkACadrfCMcszmnVTs3XwOM2Zd3Ck5xm73xk8vvMv+0zptSApxQqJqo1sfDzY/80DG20nEmhPvzdsR3PDr6FtLMqHjNo2WsU7Wa1yIMrGNcBxD1Qadw0eV28W/ux9X4aqjYPtgqAgSEi2A6dabex515utsOp2sz1PrQLnvmWf4UGXr6BuJysMO19ry7c5zbb94s/gnsV2rkf7s+HIq/0FVi3HTZnZINiekx6077NStWC++jm2Y+1wbngdyWn2fkddbwVmivPclapCzRZw8SfQzok6Ou/d4HsJ5KvpiSjymj3Pect+p2Ll3LetgAvQ+GgbKvzgFmsBAKiSDSmVQ8v1GGA/Axq4CFw9GgZutP8H98DW+78tI+Kp008GWopIU6xguAC4KJaCIpICfAG8G4hsii9l4KQuzUzTQy+0syHdJHsERI8B8JMT9FWSbdb9xXA7p4/+h3VGT48Q/HX517ZzDND8hNAfOkDb3vCHM/oKCLAzX/aPI3fTqIv9URfm2xDFdmeFTt5KToPj77PHHV0zVNueYe8X6KTcNMixfxAa6ueHe6QdMG8kpMNx90G7PqHLfwCc7UyW+mZAeHhs0x62gwtQqSrcOQ8q17SmhcHOfIH2/WyHtWuT7dD7+Nj6T/sPdL/LjhK9dHANGtzP5zaXZNQOLeOdHwGhoc9V6gSPm59gvysnD7IhnLP/Z4XGbR4TSLLTSRV4ZqWnVIbj77W+DAh2pgHOfr3k4IeWJ4Wn+U3oS8u038Pv/uX4S1zPk+Tam/2qb4ODskAYrPd+gXsG8rnNMP3egDNeCAYe3Dw1KPyzGkD/scFJe96QcBGrMcRKlVpWwA2/JVg+Fg67OHw7YO87u/Dj8ImpZUjcBIQxpkBEbgZGYcNc3zTGzBKRh4EpxpjhInIkVhBUA84QkYecyKXzgGOBGiJyhVPlFcaYGGY+VRC5pYi48JpgEpLDfRjdbrG249xtdpT9dDP/uiJpHinpdnJOQEB0u8WOWr5/yP5g3MIhEq1PhRot7SxQd8dz2ZfWj/Db4PCYf7CaQHIl+3dkCRPRvPR+Fo4bEB7R5DXP+HWMl3xu/SC/vgQtfDojETjOs1ptpscldspjoQIiqRJcPjy8rgyn481uBcfda+cdpGeHChI/EpP9hYOX7DZWwHa6KHTU3OMeey27DcwdERwciFhH8pqZNtwX4MKPoHE3a8rpcK7teMGOPHO3QfPjrSD30uMeu2RFnY7+bavT0T7riZ4lYTr6jOSj0ex4KwRqtgrVYgC63AQr/4DDXHMjAt/1Vr1Kp7FXa2L9SO6VARKTQ6PSanr8M/UOg/OH2hnXezJnqLxo3cv+xYm4egWNMSOBkZ60ga7jyVjTk7fcUMBntkl8MKXRIPaWiz8NV60Tk+2IxL1MRXIluMmxrLknRmXUtZPfTnoIah8CWSX4/d0jlZMftZ8nPVC69jY91goId8hhs+PsZ3o2vNEzvEwss839SEoJ7UDPGmL3iPA6MzNqW79Jaqa9vmOdNV1AsBNo28fOqPUjq6Fd2O0Oj9/HOzpLTCEqx95tzU3pPpOq9hQRa3f3kpQa1LjqdgyuYYRAp/MBx480cFPwWfwEdGpGeIccoGl3+FcJk9oqVYV/zo/hIWKgxYlw30r/EOfMutYn4qZNbzv5s/ezoem3/mFntUfys4jAUXvg06ra2H76LuG/B8Rj/lGc0ZnUUDon9d7Q+Bho2dOu8+ImzRnJXP9zcG0d92qpbrty2zPs+jFJabaueFOtidMenx9ew852qYUXD7fnaVnQoLNtY1nQ6Xyn4/MhYA7o4OPPATj3HSKuJ9L/p8gzcC//2pZ754zYRqkJCWUrHEpDkmOKq9spND3aOlv7EqWZ/3Lcvdas53XIVm8aXPKkLMluY827J8S422I0rvu55Gi/fRAVEPGk00VWFc/bYdfYaeCo/95Rjnek5CXgvO10YXB12Vgm7IE1UZS07lE0utxgtZnDI8w0r9EcrvzGLu5XszVcUg4uo1goqZNMrxG5U2/aPTgyL40ZoyJIrwFXfhsaRnwgk5AQt2gdX5JS4NIyXFY7LTNo6ttPKJWAEJFqQENjTPy8IhVBWS83UrWxjeJwOxivH+8se0C4gIi2SqaInSiTXDk4WS3Sfgpebpu5dzbUxOTwqKSw9iUE23kgEHDURorf35dwRyopShkTVUCIyFigj5N3KrBWRMYbY+6Ic9vKDd+tRktLViPY4qzRdPilocIB9n6UFxh5ZDkuGz9HrR+pMU6YU4JUrm4nWFVrXNEtUZQKJRYNIssYs1VErsGGnT4gIgeWBuEVEO6lC/wILIbW6lS46CPrRF493ZpZIPp+zXuzGFzO1dZs5DdJqaIIaGAH0p7AfhPYFOUgIxYBkeTMaD4PKCNvzT5O9aY2hj/S+jhVasPV3wUnKqVWCRUK0aIe9sbkk5AQ2TFbUWQ7E8m63lSx7VAUpUyJRUA8jJ3LMN4YM1lEmgF7sa7zPoh35FuQa23vKVX816DPqBu+kqO7jsIo/gG3gOjzUui15Mo2fHN/onL18El2iqLs90QVEMaYT4BPXOcLgX7xbFR5E+ZaLcq3ZqQ+L/rv/ZpRJzzNbaaK5kAOaBgtelp/hZsBUfaaUBRFKSeiBkyLSCsR+UFEZjrnHUXkX9HK7V94NIjCAmsyiuRL8M7AhVJqEI6A8FvwLTF53w+vVBTloCCWGTWvAfcC+QBOiOsFJZbY3/CamArzrFrhFRCBlTJ9Y7HdGkQUH0PgekJiyfkURVEqkFgERGVjjHfB+n14cZLSExbmWpQfqkHUP8Iuxdu0hz2v4mNiqtvJzm5OSIZut4ZfdxNYLbI8ZkIriqLsIbE4qdeLSHOcIbKInAOsimuryp0YTEyNusCYQfa4is/eE6kZ8K8IS3Sq/4MAACAASURBVIF7qdUW7l4UuhCboijKPkYsAuImYAjQRkRWAIuAS+LaqoqmMA+QcBNTYP/d0uymFYnKMU50UxRFqSBiiWJaCJwkIulAgjFmW/ybVc6E+SBy7bIRAQERuH7mf+H3ocFNTRRFUQ5gIgoIEfFdSkOc9XaMMc/EqU3lju8KQium+q+ZVNrlshVFUfZTStIg4rOH3T5JhCUiHGG4fXc+uqKRoigHGxEFhDHmofJsSIUSaQ0hR4NYsH4HnfxzKIqiHLBEDHMVkbudzxdF5AXvXyyVi0gvEZknIvNFZIDP9WNFZJqIFDjRUe5rl4vI385fhM0IyoqSBYSiKMrBSEkmpsDO6VP2pGIRSQQGAz2B5cBkERlujHHv87gUuAK4y1O2OvAAkIPtvac6Zfdi55sSiKJBlMly4IqiKPsZJZmYvnIOdzrrMRUjIrHsUN4ZmO9EQSEiHwF9gWIBYYxZ7Fwr8pQ9BRhtjNnoXB8N9AI+jOG+Zca7E5ZyWfRsiqIoBySx2FDujTHNS31gmet8uZMWC3tTttSI+GsIw6fbzdtVg1AU5WCkpDDXU4HTgPoen0Mm+8hSGyLSH+gP0KhRoz2vKEL/XxST/FQURTkwKakHXIn1P+zGbjUa+BuONQFFYwXQ0HXewEmLhZjKGmOGGGNyjDE52dk+y1/ESgQfhHFmSBwgOy0riqKUipJ8EH8Cf4rIB8aYKOtX+zIZaCkiTbGd+wXARTGWHQU8JiKBxYpOJjaz1h7iLyCKVDQoinIQE4sNpbOIjBaRv0RkoYgsEpGF0QoZYwqAm7Gd/RxgmDFmlog8LCJ9AETkSBFZDpwLvCois5yyG4FHsEJmMvBwwGEdDyL5GNTEpCjKwUwsi/W9AdyONS9F2Ww5FGPMSGCkJ22g63gy1nzkV/ZN4M3S3G+PiWBiKio2MamTWlGUg49YhshbjDHfGGPWGmM2BP7i3rIK4L2693lS1MSkKMrBSywCYoyIPC0iXUXk8MBf3FtWrlgNYUmldvCP6WFXBZiyeCNf/bkyJP3vNduYtGgj23MrJqjr7zXbaDJgBL/OX18h91cU5cAmFhPTUc5njivNACeUfXMqBuOYmAxAtcbBdFeec175DYAzOtUDYP32XHo+O674+uInTg+rd8y8tdTOSKNdvcyQ9FVbdvHz3+s5L6dhcb4PJy5lyGX2Ff86fz2dm1YnKbFk+T1hoVXkvpm5mm4takZ/UIc/l23mu9mr+ecpbWIuoyjKwUcs+0EcXx4NqVCKBYS/ScnPB+HVJvy48q3JQLjwOO/V31i2cRdndKyHwRTn251fyIwVW7jo9YncckIL7jy5dcnNDrSvlJawvoPHA3Bnz9YkJKgZTVEUf6KamESktoi8ISLfOOftROTq+DetPCnuau3H9ePpnvtsRIGRW1DIQ1/NDkkzkdZzAiYt2sglr0+koNCuKLJs4y4APp68lHYDRxXn27Qzj7Vb7a51f6/ZHlbPtzNXM2buWtc9Qz9L4rtZq5m+fHNI2tbd+WzdHR7BvHzTzhKfpzzZujufh76axe78UsVHKIpSBsTig3gbG6pazzn/C7gtXg2qCIKdoSMQ6rRnmakdMf+Xf4RrDys274qY/8b3p/HL/PWs254bkv7V9NCtvTftCHbWxkdruX7oVK58O6ht7Mizvo/3JiwpzjNx4QY+m7qcoqLQ8v3fm0qfl8aHpHV5/Ac6PvhdSNp7vy3mmCfHMHFRfKKKV27eVSwoI/HXmm2M+2sdAC/9OJ+3xi/mkynLSixTWn6dv56123aXaZ3Kwce6bbkV5oMsD2IREDWNMcOAIiie33CADeeijZaD17+duYq7Pw13ZB/z5JiIpTfvzANAPBpJgacT/3P55mJzUbQBfOdB3/PUt/PC0s8fMoE7P/mTZveNLNYO3NqAW2PYnR/eUf/oaChrtpZ957lpRx7dnviRx0bOBWDY5GW8NX6R05ZCbhg6lT+WbebkZ8dx2ZuT2JVXSF6BbaP3Xe0Nxhguen0i5/zX+pUKy7DuktiRW0C///7K3NVbS112/trte6XVzV+7vVjoRuODiUtpMmBEhWltq7fsjsmE62bmii2+2rCbwHepLDly0Pf0em5c9Iz7KbEIiB0iUgOnlxSRLsCWuLaqgijyGPP9TEzXD51WYh03fTCtuNMLEOjcujz+A1MWB0fmhUWhX9hpSzYxb/U2594w/M+VNBkwgoXrtnPHsD+K87V/YBRbd4eOWvIKivjv2AUhaZsdjWRnXvCH/upPoXnA+iTmrt7KexOWsGyT1YQeGzmHaUvt6upNBoygyYARrPRoSUs27OCxkXO46LUJAJzy7DieGf0Xc1Zt5bVxCxn45UwmLdrIpW9MZMmGHSzduBOAsfOsELr7s+k89NVs1m/PpfOg7/lm5mpe+zk4B7P/e1N4+9fFYe0NsDu/kPcnLgnp4J8d/RcPfTUrYhmA/EKbf+nGnRQVGZrfN5LHRs7xzbt0w06ueWdK1M5n1KzVHPrwd3wwcSkXvTbBVwhMWryRqUs20efF8eQXFnHHsD8YMX1V1I5/wbrtnPTMTzz3/d8l5tuZV8C2CO285cPfuezNSazblhtWJqDR7cgt4M1fFjFohDWfDp2wJOQ5bvpgGt2f+rHENpQFF742gVs+/D1mAbV+ey69X/yFjg9+x5h5a1nrM7j5a802Wv3rG0bNWl3WzWX5psjWg0jkFhTy4aSl7M4vJLcg/DnXe6wNFUUsUUx3YNdfai4i44Fs4JySi+xfiOsHWlRkwjqlWN24TQaMAGDE9FWMnLHKN497ZDRzRWgnMnf1Nj6Zurz4/Mlv7Ei7/3tTmb826JPwU2l/mLOGJ7+dG5K2cWcejWpUZuOOvOK0wWPCBcSfyzYz/I+VvOwSMGu25nL2y7+y6PHTitOmL9/C+u25XP/eVJ46pxOXvDGx+JoxhnlrtjFvzTZe+CHYkb37mzV/9Xh6bLF2lOhxjJ/6/M/FAi/fNcr7+e+Sw3cf+Xo2709cSv2qlTiudS0Annfu/cAZh/iWWbR+B9/ODHYSs1fZ/8E7vy7mvtPahuV/atRcvp+zhtGz1tDvCDun88e5a0gQKb7n9twCrntvKgD3fTEDgPu/mMlnN3Rj1ZZdJCUkUK1yMguc/2FeYRGDRszh82kr+HzaCgad1Z6ebWtTKzMNYwzPjP6LXu3rcEi9LMAKYoDPf1/O7T1bAVbr+X7OGnq2rc2gkXNoUasKj4+cw9bdBb4RdXOc55y6ZCPXD53Gfy8+nFM71KXdwFEc1zqb09rX5e7PQjXjR0dYoTnt3z2pnp7CCJdJdHd+ISOmr6Jbixr8MGct5xzRgLTkRAqLDOPnr2fZpp0c3qgabetmkldQxK8L1he/rwkLN7B9dwGHNqpK5ZREKqfYbqjJgBFcfFQjFq23z7srr5C05ETf/2NeQREFRUVUTknif78Hl2kLBHx8en1XcppUZ/z89TSqXpmJTsTf2HlrOeWQOr51xpvcgkK+/H0lvTvV5fGRc3lvwhLu/XwG1dNTuL5HM36cu5aP+nfll7/Xc8kbE3nryiM53nlnbr6ZsYq2dTN5b8ISGlarxBVHN41bm2OJYpomIj2A1ti+ct4ers20z+L2QTzx7VyGjLOj2L0xPExe7L+3UUlRQzNWBBWzxet3FPs18qPY7AFueD9cszlz8HiGXdeV8179LWr5yYv9fQ7uUev1Q6cWH7uFA8CUJdH3cgq85sQE4ZnRfxWnu0e1381e41t2sdNpuPnN+dFPXbKJHq2y+cllQpm9citbd+fz0aSlPH52R979bTGHNqzKTR/8HjI6m+T4WnILimgyYAQ3Hd+c18Yt4qe7j6NuVqVi7WvUrNXFAuKqt+0eWnMf6UVaciIfTlwa1rYNzj26Pu4/4nYPQu7/Yib3fzGTVy45gsY1KvPij/P5fNoKHu57CK+OW0hmWjJggxvu+uRPuresyVd/ruL7Of7vqqCwiEmLNrJg/Q6Oa5VNanLQUPCq892+4f1p/Lt3OwDGzlvH2HmRzU+XvD4xJFQ7t6CQYVOWMfDLoKY2e9VWcvOL+Gza8pCy5x7RgLmrtzFjxRae6teR7+esKf4f185MZeuuAi7r1phXf7Ltet/1Lldt2c3X01dyfJtafD5tBZMXb2TWyq1c2qUx//tjBUs27OT41tmM8Wn7Oa/8xvU9mvOKozG3qZMBQIIIw/9cyQltalElNYn8wiLmrNpKxwZVnXvuouvjP/LyxYdzWoe65BcWsXLzLhrXSGdXXiHXvDuZu09pQ7PsdE5xhbl/N2s1b/yyiEfObE/Tmunc/el0LunSiCMaVwdg8Jj5fD5tOQvW7QgTxBt35BWbXTdszy3+bQWEXXKi8FCf9vz011qe6tcp7Lfevn4WOU2qR/z/7Q0STb0VkZuA940xm53zasCFxpiX49KiPSQnJ8dMmbJHm98x6bNn6TzjQf7V9GOGzgmqe61lKaNSBzCvqAGn5D3lWzY1KYHcUtg2M9OSwsxD0WhdO4N5a7aVqkyAQxtW5Y9lm6Nn3E/oUD+LVVt2UTerEmu37WaNE/X1f+d24s5P/vQt06VZdSYsLJ3TvVZGKpPuP4keT49hyYadNKpemUfPbE9mpWTOdMKED6mXyYltavHD3LXMWll6v4IfvTvW5evpq6iSmlQmzs+kBAnx3+zJ98+P7i1rRtXw9nXevaoz381ezdAJSyO+l/pVK7Fi8y7euaozA7+cyZIN1kwa+L97ue+0NnRrXpPeL/4S9/YHuOropgw8o90elxeRqcaYHN9rMQiIP4wxh3rSfjfGHLbHLYoDeyUgPn2Gu++6m2lFLclzKVWVyaVjwkJ2ksr0oma+Zaunp4SYcBSonJLEzrzyjezISEtiWxl0fEp8SUpMiBrFtj8jIrSqXaXYl1he/G/kaHq13zPTWUkCIhYndaJI0Hvr7DWdskct2UfZm+iQip4uEDA/7EtUSYvFtVW2lJVwEBEqpfjbveNJ27qZJDg/s2SfGfS1M9NITy2f91qtcvx+3h3qZ1Epgl/Bj9Sk8v9f7A3GmFIJBxGhY4OqNKxWmRpVUkt9v8C7XL5pZ6nLxkIs37hRwMci8qpzfh3wbVxaU2EYxl6RTufd97OWasWpddnA2LRb+LzwGO7Iv9G35HGts0u035Y1rWpX4S/XJLq5j/QiMUE49KHv2JHnH/VxzTFNef2XRb7XApzavg7fzIwc4XFCm1pc0a0JVSsnh82n8HL/aW0ZFCEqKFb+fOBkOj30XfSMHvp0qseYuWvZtofmmVG3HcuOvALOfvnX4rTrezRnyYYdxe/n9pNa0bxWOjd/8HvU+k5sU4vXLsuh2X0jfa8f06Ims1dtZdq/e3L6Cz8za+XWELv6v3u3o02dDI5uUZN123I5ctD3YXUkJkhMobpzH+lF35fGF5srB190OB3qZ/HM6HksWr+DjLRkLu/WhG7Na3DIA8EJnH061WO4K7jC+52vk5nGaidyaNZDpxSXveWEFrz44/zifPed1ob+xzbHGMMrPy3kjE51Q8LDex1Sh289UUb/PKU1T48KD+d+64oji+cEeZl0/4k8/e284oCP205qGTUCzM3Zh9Xnc8fxfWHnhnw4yc7BSUlK4NruTXlt3CLyCovod3gDerTOpl3dTN75dTGdGlblLo+Z84puTaiSmsQ13Zty1duTWbpxJ+u3W4vDG5fn0K15zZABSe8Xfw4LXvnr0VMZNWs1C9ZtL36OPweeTEZaEgvXb2fgl7M487D47Mgci4D4J1Yo3OCcjwZej0trKhjvT2wVNTgz92HmmMjbmZ7RsV6ZCYie7WozOoKTFuDNK3I4ukVN/l6znd4v/kLtzNTiKI9ODavy6wL/RXYzomgZj53VgYuOasSCddspKDQMHjM/pENIShBeuywnLPrIy60ntOCwRtWKQ0JPblc7otM5EuP+eTzpqYlkVUrm1hNbhkREXXV0U950QogfPbM9vy3cEBJZ06xmOi9ceBj/+Oj34smMA3u3493fFrN4w07u7tWa9dvymLBwQ3H0ElgH5tzV2+h3eANa18lg6YbQ0VifTvVoVy+Ta96ZTLu6mdx6YgsAnqg21zfE8aWLDqNJjXQOqZeJeEKnR97andNe+BmAsXcdR+MalYuvFTjhtx3qZxULiOyMVI521tnKzkhlyKVH0N+JmDovpwHDpiwnPSUxzH5+ese6xe+mW/MaPNTnENKSExl1+7EsWLedR76ezfFtsqmcksRzF4Rbi0fffiz3fj6DKUs2cXvPVpx9eH2ueGsyw67rSuem1Ysj9r66+RgqpSSwPbeQtVt3h2g5d57cmjHz1jJzxdZihz7YUfMNxzUH4Kl+HYudtq9cegRj5q5l08485q7eRvX0FK45pmmxgAjk/eCao+javAb/Or0tpxxSh+5Phc5BqpWRVrxMzW09W1G/aiWa1kzn6BY1eWzEHD7/fQWXdmlMQVERn01bwYfXHkVWpWRmrNhCz3Z1qJKaRMvaGXRqmMVRTWuwfnserWtncNcpts4LOzdizdZcjmgcHEw+cmZ7AKpVTmb99lyWbNhJ05rpnJsT3Bjz8xuPBmzEYeem1X1/l1/f0p1deYVs3pXH1l0FFBQVkZKUULwGXE7j6tTKTCWrsi3bolYGH1zbJayesqJEAeGYk2YZY9oAr8StFRWNj50o4Nz7w7TwLRJwXrWrlxl19O0lJTGBOY/0ovl9IzmtQx1GzlhN27qZvHZZTvEPz48T2tjZ3c2y0wFCQuC8MeNP9uvAPZ/ZkEt3JxQgOyOV5ARh5ZbdtKlrIzyaZ1cBwk0cp3aoGyIcUhITyCssIkGgyNgObcaKLXRpXoNuzWuSW1DI5V0bc+PxLTikXhandqjDyU7Ex5VHNyFBhKuPacrDX83mhuOa06ZuBs+M/otlG3fSyNXWO3q24tf565myZBOXdGnEwDPacdPxzRk8ZgHn5TTk4qMahQiIVy49ArAC7/wjG1K1Ugrt6mVy5dFNmLZ0M4c3qoqIsCuvkB/nruWQetas08jzfupkpdG6dgaXd2vCEY2r0dqJgHn98iND8v1yzwn0em4cc1dvIz0lsViD692xHl6+va07m3bk065eZnFgQ5Oa6SF5AtFq7etnFWsFzbND85x8SB3a1c1k9qqtnHlYfYZNWU7llKCDdeSt3UlNTiCrUjJNa6Rz1TFNqVY5OURQNc+uwttXdg5ro5uWtTP49IZubN6ZR9XKKTStmc6ch3uFmd86NMgKK5uRlkS/w23E19e3dC/xPucd2TAkquf4NuFhna9flkO19BSOaFyNfkc0KP4uXtPd+gXb1s1kzqqtDOzdrrh9dbLSePrcTsV19D3UjrCfOf9Qnjk/6FJ9/OyOxcctamUUHwcEGMBrl4Wa5xtUq0yDauG/KYAT20ZegSHWPJVSEqmUUom64a+WY1rGvihnWVCigDDGFIrIPBFpZIwJj+U7YPAstYGNTiqIYLKpX7US6anBH8p5RzYMExCVUxJJECGrUnLYMhzDru9KYoKw+InTMcYwdMKSsE7l0i6NOa51Nle/Yx3vP999vKvuJH679wRqpAdtlu5Z0ekpifRsV4fXfl5E74516XtoPR75ejYbXM70yfefxNbd+Xw7czWHNawacu+UJPseAqaE1KRQgVErM5Xlm3bx7lVHkZ6ayMtjFzBjxRZqZaQ67y6Rh/raEdU/TmoJQFpyArvzi0LmJwQ6dIB7Tw2fgwDw/rVHsTO3kKrOiKlGldSQiI0PrjmKnXmFfDV9ZbGAS09Nolvz4A9JREJGe5VSEjm9Y13f+9nnT2DU7cdGvO7mtpNacv3QaRzdoibfzV5Ddoa/HblNnWCY6M/3HM/mneGR4oHZ6y1rZ/DeVZ35YNJS2tbJDMv3+uU5TF68kfpVKwGh80rc4aiBEe/eUNXlj3ALhzF3HceqLf4TxGY8GMuW9UFOblebohKceSe1C3aoflrsFzd2Y3d+YUhblbIhFhNTNWCWiEwCioPRjTF94taq8sZnNVe71HbkmZyBUXZBoeH41rWYdN+JdH9qTHHIa1pyItP+3ZPHRs4pnldRtXIyQ68+ivb1g0MDEeHSrk3C6g+orAEaVg8dsdTNqhRyvtuZjXldj2Zc3Lkx1dNT+P6OHsXXR9zanRkrtnDtu1OKR6WZacnFS467ueropnw3aw2PndWBjycv48qjQ9t3aZfGPP7NXFrUqkKdrDSe6teRsR3WhozAvPx4Z+QOpSRSkxJLdFQGljl3dyLlSa/2dVn8xOms3LyLXfmFvHRh9K1SamWkUSsjLSz9pYsO56s/V9KkRmWa1kyPuIR7vaqV6HtofbY4QubYVjX5dcGG4lFyedC0ZjpNPRrQnjLkMt8AmphJS06MOKFO2TtiERD/3tPKRaQX8DyQCLxujHnCcz0VeBc4AtgAnG+MWSwiyVg/x+FOG981xjy+p+2Ijms/CIfkxMj29quOaVo8UzrfWS6jVmYa/Y9tVuyUC8Sw33lyKxJEeOWnBTSukR4iHMqS3Y62c+4RDcJMJmBV7jpZaTx7fqeQ0bUfLWtnMPXfPQGKZ+666X9sM87LaUi1dDtiq5aewlmH+e4cW0y9qpWoV7VSiXn2Z+pVrcR7Vx8VPWMJHN+mlq+JJRJZlZP56Z92Ql9Kku6frpQ9Ub9VxpifgMVAsnM8GSh5QSKK/ReDgVOBdsCFIuKdzXE1sMkY0wJ4FnjSST8XSDXGdMAKj+tEpEkMz7Nn+GgQKRE263n87A5cdXQTnjv/UC7p0ohODYLmGbcKfuah1mSUmpTI6R2sOaN+1fBRY1kR0Fyihb2edVgDamfuXTtEpFg4KBVL4xrpKhyUuBHLfhDXAp8CgTDX+sD/Yqi7MzDfGLPQGJMHfAT09eTpC7zjHH8KnOjMuTBAuogkAZWAPKBspqr6ELKjnEOy50f3wTV2dHhS29qICA2rV+bRMzuE2EQPdWz5g85qz2NndShOb18/k6f6deSJfh0pLUMuPYKP+0ePUrjvtLZUSk7UjltRlDIjFhPTTdjOfiKAMeZvEYlFD64PuBfxX05w+9KwPMaYAhHZAtTACou+wCqgMnC7MSZsrQQR6Q/0B2jUKHIoaqxE0iC6NqtBtxY1fRdBc9OteU3GDzih2HnoaifnHRlu6/fj57uPD1mv6eQYFxbrd0SD4rWCFEVRyoJYdNNcRwMAwBnVx3v+cGesh7ge0BS4U0TC1rowxgwxxuQYY3Kys7P34nbhj+MO9SwsxXRpr3AoLQ2rV97rOhRFUcqCWATETyJyH1BJRHoCnwBfxVBuBeAeNjdw0nzzOIInC+usvgj41hiTb4xZC4wH9i7UoST8fBAuE5N3dzZFUZSDgVgExABgHTADO6N6JPCvGMpNBlqKSFMRSQEuwO4r4WY4cLlzfA7wo7EOgaXACQAikg50AeYSN8J9EM1cE5RKitFWFEU5UIllP4giEXkH64Mw2P0govaYjk/hZuxaTonAm8aYWSLyMDDFGDMceAN4T0TmAxuxQgRs9NNbIjILO3vtLWNM+D6fZYVrP4jEBOGlCw+jR+tsWtXO4Ilv5lKo8kFRlIOQqAJCRE7HLrOxANtZNxWR64wx30Qra4wZidU43GkDXce7sSGt3nLb/dLjR9DEVGQMpzphqV2b1QDUxKQoysFJLFFM/wccb4yZDyAizYERQFQBsb9hCF2WKRDCWl6b2iuKouxLxOKD2BYQDg4LgfLdDSPeRLCYBdY3Ux+EoigHI7FoEFNEZCQwDDvIPheYLCJnAxhjPo9j+8qJ8CgmCM6F8C5WpyiKcjAQi4BIA9YAgZXf1mFnN5+B7Vn3fwHhE+YK0KJWFW47qSXn6AQ0RVEOQmKJYrqyPBpSofgstQF2BvRtJ4UvVqcoinIwoLYTgoLBq0EoiqIczKiAADB2JVQVEIqiKEFUQCiKoii+RPRBiMgdJRU0xjxT9s2pKDSMVVEUxUtJTurA/pGtgSMJrqN0BjApno0qb8SRD2piUhRFCRJRQBhjHgIQkXHA4caYbc75g9iZ1AcMBvVBKIqieInFB1Ebu6NbgDwn7cAhQpiroijKwUwsE+XeBSaJyBfO+ZkEtwk9oFANQlEUJUgsE+UGicg3QHcn6UpjzO/xbVY5E2EmtaIoysFMrGGulYGtxpjngeUi0jSObaow1MSkKIoSJKqAEJEHgHuAe52kZGBoPBtV/gRFw/k5DUvIpyiKcvAQiwZxFtAH2AFgjFlJMAT2wMBlYnrynI4V3BhFUZR9g1gERJ6zxaiB4j2iDzCCW44qiqIollgExDAReRWoKiLXAt8Dr8dSuYj0EpF5IjJfRAb4XE8VkY+d6xNFpInrWkcR+U1EZonIDBFJi+2RSo84GsR3tx8br1soiqLsd8QSxfQfEekJbMXOqh5ojBkdrZyIJAKDgZ7AcuwmQ8ONMbNd2a4GNhljWojIBcCTwPkikoT1c1xqjPlTRGoA+aV9uFgxGIqM0Kr2gWU5UxRF2RticVI/aYwZbYz5pzHmLmPMaBF5Moa6OwPzjTELjTF5wEdAX0+evgTnVHwKnCgiApwMTDfG/AlgjNlgjCmM9aFKjTEawaQoiuIhFhNTT5+0U2MoVx9Y5jpf7qT55jHGFABbgBpAK8CIyCgRmSYid/vdQET6i8gUEZmybt26GJoUGZ0DoSiKEkpJq7neANwINBOR6a5LGcD4cmjXMdhFAncCP4jIVGPMD+5MxpghwBCAnJycvVACVH9QFEXxUpIP4gPgG+BxwO1g3maM2RhD3SsA96SCBk6aX57ljt8hC9iA1TbGGWPWA4jISOBw4AfigTGqQSiKoniIaGIyxmwxxiw2xlxojFkC7MIOtauISKMY6p4MtBSRpiKSAlxAcMnwAMOBy53jc4AfnZDaUUAHEansCI4ewGzihvogFEVRvESNYhKRM4BngHrAWqAxMAc4pKRyxpgCEbkZ29knAm8aTrPSBgAAEchJREFUY2aJyMPAFGPMcOAN4D0RmQ9sxAoRjDGbROQZrJAxwEhjTPyWGLczPOJWvaIoyv5ILKu5Pgp0Ab43xhwmIscDl8RSuTFmJDDSkzbQdbwbODdC2aGU25IeRWpiUhRF8RBLFFO+MWYDkCAiCcaYMUBOnNtVroiGuSqKooQRiwaxWUSqAOOA90VkLc66TAcSqkEoiqKEEosG0RfroL4d+BZYgN2XWlEURTmAiWWpjR0AIpIJfBX3FlUERn0QiqIoXmKJYroOeAjYDRRhw30M0Cy+TVMURVEqklh8EHcB7QOT1g5MdKKcoiiKl1h8EAuwy10cuOhMakVRlDBi0SDuBX4VkYlAbiDRGHNr3FpV7miYq6IoipdYBMSrwI/ADKwP4oDEiGoQiqIobmIREMnGmDvi3pKKxKj+oCiK4iUWH8Q3zr4LdUWkeuAv7i0rRwSDrsWkKIoSSiwaxIXO572utAMrzFWX2lAURQkjlolyTcujIRWLRjEpiqJ4KWlHuROMMT+KyNl+140xn8evWeWPCghFUZRQStIgemCjl/zWXTLAgSMgTGCCuKIoihIgooAwxjzgHD5sjFnkviYiB5zZSX0QiqIoocQSxfSZT9qnZd0QRVEUZd8iooAQkTYi0g/IEpGzXX9XAGmxVC4ivURknojMF5EBPtdTReRj5/pEEWniud5IRLaLyF2leqpSo05qRVEULyX5IFoDvYGqhPohtgHXRqtYRBKBwUBPYDkwWUSGG2Nmu7JdDWwyxrQQkQuAJ4HzXdefAb6J5UH2Cl2LSVEUJYySfBBfAl+KSFdjzG97UHdnYL4xZiGAiHyE3XzILSD6Ag86x58CL4mIGGOMiJwJLKIcdq8T9UAoiqKEEYsP4iwRyRSRZBH5QUTWicglMZSrDyxznS930nzzGGMKgC1ADWeL03uw+1DEH9UgFEVRwohFQJxsjNmKNTctBloA/4xno7BaxbPGmO0lZXKWAJkiIlPWrVu3F7dTAaEoiuIlpsX6nM/TgU+MMVsktpVPVwANXecNnDS/PMtFJAnIAjYARwHniMhTWB9IkYjsNsa85C5sjBkCDAHIyclRO5GiKEoZEouA+EpE5gK7gBtEJBu7/Wg0JgMtnTkTK4ALgIs8eYYDlwO/AecAPxpjDNA9kEFEHgS2e4VDmaKruSqKooQR1cRkjBkAdANyjDH52N3l+sZQrgC4GRgFzAGGGWNmicjDItLHyfYG1ucwH7gDCAuFLS/UxKQoihJKSWsx3W2Meco5PdEY8wmAMWaHiNwP3BetcmPMSGCkJ22g63g3cG6UOh6Mdp+9RdQHoSiKEkZJGsQFruN7Pdd6xaEtFYfR/SAURVG8lCQgJMKx3/l+ju4HoSiK4qUkAWEiHPud7/fontSKoiihlBTF1ElEtmK1hUrOMc55TGsx7T8ccPJOURRlrylpqY3E8mxIRSLqg1AURQkjlpnUBwHqg1AURfGiAsJBw1wVRVFCUQEBGuaqKIrigwoIdKKcoiiKHyogFEVRFF9UQAAa5qooihKOCgiwGwbpRDlFUZQQVECgPghFURQ/VEAA1sSkAkJRFMWNCggAo14IRVEULyogANUgFEVRwlEB4aA+CEVRlFBUQGCd1IqiKEoocRUQItJLROaJyHwRCdtvWkRSReRj5/pEEWnipPcUkakiMsP5PCGe7dSlNhRFUcKJm4AQkURgMHAq0A64UETaebJdDWwyxrQAngWedNLXA2cYYzoAlwPvxaudFl3NVVEUxUs8NYjOwHxjzEJjTB7wEdDXk6cv8I5z/ClwooiIMeZ3Y8xKJ30WdsOi1Di2VSfKKYqieIingKgPLHOdL3fSfPMYYwqALUANT55+wDRjTK73BiLSX0SmiMiUdevW7XFDRaOYFEVRwtinndQicgjW7HSd33VjzBBjTI4xJic7O3vPb2R0JrWiKIqXeAqIFUBD13kDJ803j4gkAVnABue8AfAFcJkxZkEc26koiqL4EE8BMRloKSJNRSQFuAAY7skzHOuEBjgH+NEYY0SkKjACGGCMGR/HNgIa5qooiuJH3ASE41O4GRgFzAGGGWNmicjDItLHyfYGUENE5gN3AIFQ2JuBFsBAEfnD+asVr7aii/UpiqKEkRTPyo0xI4GRnrSBruPdwLk+5R4FHo1n2zw3BI1iUhRFCWGfdlKXF4IutaEoiuJFBQSga7kqiqKEowICUB+EoihKOCogilEBoSiK4kYFBCBGTUyKoiheVEAAamJSFEUJRwUEzkQ5DXNVFEUJQQWEgxqZFEVRQlEBQcAHoRqEoiiKGxUQgPogFEVRwlEBEUB9EIqiKCGogADUA6EoihKOCggCazEpiqIoblRAgF3NVX0QiqIoIaiAQPekVhRF8UMFBAAGo05qRVGUEFRAoLqDoiiKHyogHHQehKIoSihxFRAi0ktE5onIfBEZ4HM9VUQ+dq5PFJEmrmv3OunzROSUeLYTXc1VURQljLgJCBFJBAYDpwLtgAtFpJ0n29XAJmNMC+BZ4EmnbDvgAuAQoBfwslNffNqqTmpFUZQw4qlBdAbmG2MWGmPygI+Avp48fYF3nONPgRNFRJz0j4wxucaYRcB8p744oU5qRVEUL/EUEPWBZa7z5U6abx5jTAGwBagRY1lEpL+ITBGRKevWrdvjhm6s3ZUddeIofxRFUfZDkiq6AXuDMWYIMAQgJydnjx0JXa99vszapCiKcqAQTw1iBdDQdd7ASfPNIyJJQBawIcayiqIoShyJp4CYDLQUkaYikoJ1Og/35Bn+/+2df4wV1RXHP19ApGIrINYgWnZRrCWaIiDBlLZoqVrTqG0wgZIAljb1Z6sNbaA2jTVp44/aWH9Urai0llookEppFVvEHzEpsPgDFmUBBakURUVBTSSsnP5xz4PhObssu2/73r53Pslk75x75849c2bfmbn3zrnAFE+PBx43M3P5BJ/lVA8MAVZ0YluDIAiCIjqti8nMmiVdCSwBugP3m9laSdcDDWa2CLgPeFDSRmAHyYng5eYBLwLNwBVm9lFntTUIgiD4OLIq+QZg5MiR1tDQUO5mBEEQdCkkrTKzkXl58SV1EARBkEs4iCAIgiCXcBBBEARBLuEggiAIglyqZpBa0pvAqx2ooj/wVoma01WoNZ1rTV8InWuFjug8yMyOycuoGgfRUSQ1tDSSX63Ums61pi+EzrVCZ+kcXUxBEARBLuEggiAIglzCQeznd+VuQBmoNZ1rTV8InWuFTtE5xiCCIAiCXOINIgiCIMglHEQQBEGQS807CEnnSWqStFHSjHK3pyNIOkHSMkkvSlor6Qcu7yfpn5I2+N++Lpek21z31ZKGZ+qa4uU3SJrS0jkrAUndJT0nabHv10ta7nrN9XDzePj4uS5fLqkuU8dMlzdJOrc8mrQNSX0kzZe0TtJLks6sARtf4/d0o6SHJPWqNjtLul/SdkmNGVnJ7CpphKQ1fsxtUhvWWTazmt1IYchfBgYDPYEXgKHlblcH9BkADPf0J4H1wFDgJmCGy2cAN3r6fOARQMBoYLnL+wGv+N++nu5bbv1a0fuHwJ+Axb4/D5jg6buByzx9OXC3pycAcz091G1/OFDv90T3cuvVir6/B77j6Z5An2q2MWm54U3AJzL2nVptdga+BAwHGjOyktmVtKbOaD/mEeBrB21TuS9KmQ1yJrAksz8TmFnudpVQv4eBrwJNwACXDQCaPH0PMDFTvsnzJwL3ZOQHlKukjbTa4FLgbGCx3/xvAT2KbUxam+RMT/fwciq2e7ZcpW2kVRc34RNMim1XpTYurFHfz+22GDi3Gu0M1BU5iJLY1fPWZeQHlGtpq/UupsKNV+A1l3V5/LX6dGA5cKyZbfOs14FjPd2S/l3putwK/BjY6/tHA++aWbPvZ9u+Ty/P3+nlu5K+9cCbwAPerTZLUm+q2MZmthX4FbAF2Eay2yqq284FSmXXgZ4ulrdKrTuIqkTSkcAC4Goz25XNs/T4UBVzmyV9HdhuZqvK3Zb/Iz1I3RB3mdnpwAekrod9VJONAbzf/UKSczwO6A2cV9ZGlYFy2LXWHcRW4ITM/vEu67JIOozkHOaY2UIXvyFpgOcPALa7vCX9u8p1+QJwgaTNwJ9J3Uy/AfpIKiynm237Pr08/yjgbbqOvpCe/F4zs+W+P5/kMKrVxgDjgE1m9qaZ7QEWkmxfzXYuUCq7bvV0sbxVat1BrASG+GyInqQBrUVlblO78VkJ9wEvmdmvM1mLgMJshimksYmCfLLPiBgN7PTX2SXAOZL6+tPbOS6rKMxsppkdb2Z1JNs9bmaTgGXAeC9WrG/hOoz38ubyCT77pR4YQhrQqzjM7HXgP5I+66KvkNZur0obO1uA0ZKO8Hu8oHPV2jlDSezqebskjfZrODlTV8uUe1Cm3BtpNsB60oyGa8vdng7qMob0CroaeN6380n9r0uBDcC/gH5eXsCdrvsaYGSmrm8DG327pNy6tUH3seyfxTSY9I+/EfgLcLjLe/n+Rs8fnDn+Wr8OTbRhdkeZdR0GNLid/0qarVLVNgZ+DqwDGoEHSTORqsrOwEOkMZY9pDfFaaW0KzDSr9/LwB0UTXTI2yLURhAEQZBLrXcxBUEQBC0QDiIIgiDIJRxEEARBkEs4iCAIgiCXcBBBEARBLuEggopAkkm6JbM/XdJ1Jap7tqTxBy/Z4fNc7NFVl7Wx/D8k9SnRud8/SH4fSZdn9o+TNL8U5w6ql3AQQaWwG/impP7lbkiWzJe6bWEa8F0zO6sthc3sfDN7t30tO2T6kKKcFs79XzPrdKcZdG3CQQSVQjNpXd1rijOK3wAKT8uSxkp6UtLDkl6RdIOkSZJWeNz7EzPVjJPUIGm9x3AqrCNxs6SVHlP/e5l6n5a0iPTFbnF7Jnr9jZJudNnPSB8q3ifp5qLyAyQ9Jel5P+aLLt8sqb+kOqW1HWZ7++ZIGifpGY/pP8rLXydpeqbeRmXWOnDZkZKWSnrW23ihZ90AnOhtuNnP2ejH9JL0gJd/TtJZLp8qaaGkR70dN2Wu22w//xpJH7NZUB0cytNREHQ2dwKrCz9EbeTzwOeAHaTY97PMbJTSYklXAVd7uTpgFHAisEzSSaRwAzvN7AxJhwPPSHrMyw8HTjWzTdmTSToOuBEYAbwDPCbpIjO7XtLZwHQzayhq47dI4Q5+Iak7cESOHicBF5O+gl3px4wBLgB+AlzUxuvxIfANM9vlb2P/dkc3w/UZ5nrUZY65ghQL7jRJp7hOJ3veMFJU4N1Ak6TbgU8DA83sVK+rJN1kQeURbxBBxWAp8uwfgO8fwmErzWybme0mhRAo/MCvITmFAvPMbK+ZbSA5klNIcWomS3qeFBb9aFJ8HoAVxc7BOQN4wlLguGZgDmmhl1bbCFziYyqnmdl7OWU2mdkaM9sLrAWWWgpzUKzHwRDwS0mrSaEZBrI/RHRLjAH+CGBm64BXgYKDWGpmO83sQ9Lb1CDS9Rss6XZJ5wG7cuoMqoBwEEGlcSupL793RtaM36uSupFWUSuwO5Pem9nfy4FvyMUxZYz0Y3qVmQ3zrd7MCg7mgw5pkT2R2VMkJ7IVmC1pck6xtuix7zo4vXLqmQQcA4zwt4U3WijXVrLt+oi0QM87pDe3J4BLgVkdqD+oYMJBBBWFme0gLSU5LSPeTOrSgdTlclg7qr5YUjcflxhMCta2BLhMKUQ6kk5WWnynNVYAX/axg+6klbmebO0ASYOAN8zsXtKP6fDWyrfC5sKxSmsQ1+eUOYq0RsYeH0sY5PL3SMvQ5vE0ybHgXUufIV2fXLzrqpuZLQB+Svv1CSqcGIMIKpFbgCsz+/cCD0t6AXiU9j3dbyH9uH8KuNTMPpQ0i9R986wkkVZqa7Wv38y2SZpBCjUt4O9mdrCwyWOBH0naA7xPGvtoDwtIXWJrSV1i63PKzAH+JmkNKeLrOm/32z7o3Uhaj/jOzDG/Be7yY5qBqWa2Wy2vaT+QtKJd4QFzZjv1CSqciOYaBEEQ5BJdTEEQBEEu4SCCIAiCXMJBBEEQBLmEgwiCIAhyCQcRBEEQ5BIOIgiCIMglHEQQBEGQy/8AYahMRu4yUuUAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "id": "xKDzKLo_kHAm",
        "outputId": "a7ba89f7-0099-4386-e745-7684e50e164d"
      },
      "source": [
        "plt.plot(np.arange(10,10000,10), q2_star[:-1,0], zorder=1)\n",
        "plt.plot(np.arange(10,10000,10), q2_star[:-1,1], zorder=1)\n",
        "plt.xlabel(\"Number of simulations\")\n",
        "plt.ylabel(\"Estimated percentiles\")\n",
        "plt.title(\"Normal distribution\")\n",
        "plt.hlines(xi + sigma*np.sqrt((nu-2)/nu)*t.ppf(yps[0], df=nu), xmin=0, xmax=10000-1, zorder=2)\n",
        "plt.hlines(xi + sigma*np.sqrt((nu-2)/nu)*t.ppf(yps[1], df=nu), xmin=0, xmax=10000-1, zorder=2)\n",
        "plt.show()"
      ],
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "w3JQS1volQjn"
      },
      "source": [
        "#Example p. 29: Density estimation"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "nIlQDTTylU1J"
      },
      "source": [
        "alpha = 3\n",
        "beta = 1\n",
        "h = [0.05,0.2,0.3,0.5]\n",
        "\n",
        "m = 1000\n",
        "x_star = gamma.rvs(alpha, size=m, scale=beta)\n",
        "s_star = np.std(x_star)\n",
        "x = np.arange(0, 10, 0.01)\n",
        "f_hat = np.zeros((len(h), len(x)))"
      ],
      "execution_count": 12,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "P4FDxd5DmSTS"
      },
      "source": [
        "for i in range(len(x)):\n",
        "  for j in range(len(h)):\n",
        "    f_hat[j][i] = sum(norm.pdf((x_star-x[i])/(h[j]*s_star)))/(m*h[j]*s_star)"
      ],
      "execution_count": 13,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "A5gZTKtom62s",
        "outputId": "39e8f0cf-4c19-4eae-f236-6b87740b8866"
      },
      "source": [
        "plt.plot(x, gamma.pdf(x, alpha, scale=beta))\n",
        "plt.plot(x, f_hat[0], '-')\n",
        "plt.plot(x, f_hat[1], '-.')\n",
        "plt.plot(x, f_hat[2], ':')\n",
        "plt.plot(x, f_hat[3], '--')\n",
        "plt.show()"
      ],
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KOdthjq2ueY8"
      },
      "source": [
        "# Example p. 38/39:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2qdJh5Y9ufdh"
      },
      "source": [
        "xi = 0.005\n",
        "sigma = 0.05\n",
        "rho = [-0.9,0,0.5,0.9,0.99]\n",
        "alpha = 1\n"
      ],
      "execution_count": 117,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "awxYXDt1uqTh"
      },
      "source": [
        "m = 100\n",
        "R1_star = np.zeros((m, len(rho)))\n",
        "R2_star = np.zeros((m, len(rho)))\n",
        "for i in range(len(rho)):\n",
        "  eta = np.random.normal(size=(m, 2))\n",
        "  R1_star[:,i] = np.exp(xi+sigma*eta[:,0])-1\n",
        "  R2_star[:,i] = np.exp(xi+sigma*(rho[i]*eta[:,0]+np.sqrt(1-np.power(rho[i],2))*eta[:,1]))-1"
      ],
      "execution_count": 120,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1LdMVvMsvuEt"
      },
      "source": [
        "m = 100\n",
        "R3_star = np.zeros((m, len(rho)))\n",
        "R4_star = np.zeros((m, len(rho)))\n",
        "for i in range(len(rho)):\n",
        "  eta = np.random.normal(size=(m, 2))\n",
        "  z_star = gamma.rvs(alpha, size=m, scale=1/alpha)\n",
        "  sigma_star = sigma*z_star \n",
        "  R3_star[:,i] = np.exp(xi+sigma_star*eta[:,0])-1\n",
        "  R4_star[:,i] = np.exp(xi+sigma_star*(rho[i]*eta[:,0]+np.sqrt(1-np.power(rho[i],2))*eta[:,1]))-1"
      ],
      "execution_count": 122,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 623
        },
        "id": "ruJF6Dq1wvpQ",
        "outputId": "79dda15c-0cdf-4ce3-f57a-0f60df263dda"
      },
      "source": [
        "fig, axs = plt.subplots(2, 5, figsize=(10, 10))\n",
        "for i in range(len(rho)):\n",
        "  axs[0][i].scatter(R1_star[:, i], R2_star[:, i])\n",
        "  axs[0][i].set_title(f'Const. vol. \\n rho={rho[i]}')\n",
        "  axs[1][i].scatter(R3_star[:, i], R4_star[:, i])\n",
        "  axs[1][i].set_title(f'Stoch. vol. \\n rho={rho[i]}')"
      ],
      "execution_count": 134,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x720 with 10 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}