{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# The Central Limit Theorem\n", "\n", "Elements of Data Science\n", "\n", "by [Allen Downey](https://allendowney.com)\n", "\n", "[MIT License](https://opensource.org/licenses/MIT)" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import pandas as pd\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# If we're running on Colab, install empiricaldist\n", "# https://pypi.org/project/empiricaldist/\n", "\n", "import sys\n", "IN_COLAB = 'google.colab' in sys.modules\n", "\n", "if IN_COLAB:\n", " !pip install empiricaldist" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The Central Limit Theorem\n", "\n", "According to our friends at [Wikipedia](https://en.wikipedia.org/wiki/Central_limit_theorem):\n", "\n", "> The central limit theorem (CLT) establishes that, in some situations, when independent random variables are added, their properly normalized sum tends toward a normal distribution (informally a bell curve) even if the original variables themselves are not normally distributed.\n", "\n", "This theorem is useful for two reasons:\n", "\n", "1. It offers an explanation for the ubiquity of normal distributions in the natural and engineered world. If you measure something that depends on the sum of many independent factors, the distribution of the measurements will often be approximately normal.\n", "\n", "2. In the context of mathematical statistics it provides a way to approximate the sampling distribution of many statistics, at least, as Wikipedia warns us, \"in some situations\".\n", "\n", "In this notebook, we'll explore those situations." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Rolling dice\n", "\n", "I'll start by adding up the totals for 1, 2, and 3 dice.\n", "\n", "The following function simulates rolling a six-sided die." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "def roll(size):\n", " return np.random.randint(1, 7, size=size)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If we roll it 1000 times, we expect each value to appear roughly the same number of times." ] }, { "cell_type": "code", "execution_count": 57, "metadata": {}, "outputs": [], "source": [ "sample = roll(1000)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here's what the PMF looks like." ] }, { "cell_type": "code", "execution_count": 58, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from empiricaldist import Pmf\n", "\n", "pmf = Pmf.from_seq(sample)\n", "pmf.bar()\n", "plt.xlabel('Outcome')\n", "plt.ylabel('Probability');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To simulate rolling two dice, I'll create an array with 1000 rows and 2 columns." ] }, { "cell_type": "code", "execution_count": 59, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(1000, 2)" ] }, "execution_count": 59, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a = roll(size=(1000, 2))\n", "a.shape" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And then add up the columns." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(1000,)" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sample2 = a.sum(axis=1)\n", "sample2.shape" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The result is a sample of 1000 sums of two dice. Here's what that PMF looks like." ] }, { "cell_type": "code", "execution_count": 60, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "pmf2 = Pmf.from_seq(sample2)\n", "pmf2.bar()\n", "plt.xlabel('Outcome')\n", "plt.ylabel('Probability');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And here's what it looks like with three dice." ] }, { "cell_type": "code", "execution_count": 61, "metadata": {}, "outputs": [], "source": [ "a = roll(size=(1000, 3))\n", "sample3 = a.sum(axis=1)" ] }, { "cell_type": "code", "execution_count": 62, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "pmf3 = Pmf.from_seq(sample3)\n", "pmf3.bar()\n", "plt.xlabel('Outcome')\n", "plt.ylabel('Probability');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "With one die, the distribution is uniform. With two dice, it's a triangle. With three dice, it starts to have the shape of a bell curve.\n", "\n", "Here are the three PMFs on the same axes, for comparison." ] }, { "cell_type": "code", "execution_count": 63, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "pmf.plot(label='1 die')\n", "pmf2.plot(label='2 dice')\n", "pmf3.plot(label='3 dice')\n", "plt.xlabel('Outcome')\n", "plt.ylabel('Probability')\n", "plt.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Gamma distributions\n", "\n", "In the previous section, we saw that the sum of values from a uniform distribution starts to look like a bell curve when we add up just a few values.\n", "\n", "Now let's do the same thing with values from a gamma distribution.\n", "\n", "NumPy provides a function to generate random values from a gamma distribution with a given mean." ] }, { "cell_type": "code", "execution_count": 64, "metadata": {}, "outputs": [], "source": [ "mean = 2\n", "gamma_sample = np.random.gamma(mean, size=1000)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here's what the distribution looks like, this time using a CDF." ] }, { "cell_type": "code", "execution_count": 76, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from empiricaldist import Cdf\n", "\n", "cdf1 = Cdf.from_seq(gamma_sample)\n", "cdf1.plot()\n", "\n", "plt.xlabel('Outcome')\n", "plt.ylabel('CDF');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It doesn't look like like a normal distribution. To see the differences more clearly, we can plot the CDF of the data on top of a normal model with the same mean and standard deviation." ] }, { "cell_type": "code", "execution_count": 77, "metadata": {}, "outputs": [], "source": [ "from scipy.stats import norm\n", "\n", "def plot_normal_model(sample, **options):\n", " \"\"\"Plot the CDF of a normal distribution with the\n", " same mean and std of the sample.\n", " \n", " sample: sequence of values\n", " options: passed to plt.plot\n", " \"\"\"\n", " mean, std = np.mean(sample), np.std(sample)\n", " xs = np.linspace(np.min(sample), np.max(sample))\n", " ys = norm.cdf(xs, mean, std)\n", " plt.plot(xs, ys, alpha=0.4, **options)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here's what that looks like for a gamma distribution with mean 2." ] }, { "cell_type": "code", "execution_count": 78, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from empiricaldist import Cdf\n", "\n", "plot_normal_model(gamma_sample, color='C0', label='Normal model')\n", "cdf1.plot(label='Sample 1')\n", "\n", "plt.xlabel('Outcome')\n", "plt.ylabel('CDF');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There are clear differences between the data and the model. Let's see how that looks when we start adding up values.\n", "\n", "The following function computes the sum of gamma distributions with a given mean." ] }, { "cell_type": "code", "execution_count": 79, "metadata": {}, "outputs": [], "source": [ "def sum_of_gammas(mean, num):\n", " \"\"\"Sample the sum of gamma variates.\n", " \n", " mean: mean of the gamma distribution\n", " num: number of values to add up\n", " \"\"\"\n", " a = np.random.gamma(mean, size=(1000, num))\n", " sample = a.sum(axis=1)\n", " return sample" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here's what the sum of two gamma variates looks like:" ] }, { "cell_type": "code", "execution_count": 80, "metadata": {}, "outputs": [], "source": [ "gamma_sample2 = sum_of_gammas(2, 2)\n", "cdf2 = Cdf.from_seq(gamma_sample2)" ] }, { "cell_type": "code", "execution_count": 81, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_normal_model(gamma_sample, color='C0')\n", "cdf1.plot(label='Sum of 1 gamma')\n", "\n", "plot_normal_model(gamma_sample2, color='C1')\n", "cdf2.plot(label='Sum of 2 gamma')\n", "\n", "plt.xlabel('Total')\n", "plt.ylabel('CDF')\n", "plt.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The normal model is a better fit for the sum of two gamma variates, but there are still evident differences. Let's see how big `num` has to be before it converges.\n", "\n", "First I'll wrap the previous example in a function." ] }, { "cell_type": "code", "execution_count": 82, "metadata": {}, "outputs": [], "source": [ "def plot_gammas(mean, nums):\n", " \"\"\"Plot the sum of gamma variates and a normal model.\n", " \n", " mean: mean of the gamma distribution\n", " nums: sequence of sizes\n", " \"\"\"\n", " for num in nums:\n", " sample = sum_of_gammas(mean, num)\n", "\n", " plot_normal_model(sample, color='gray')\n", " Cdf.from_seq(sample).plot(label=f'num = {num}')\n", "\n", " plt.xlabel('Total')\n", " plt.ylabel('CDF')\n", " plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "With `mean=2` it doesn't take long for the sum of gamma variates to approximate a normal distribution." ] }, { "cell_type": "code", "execution_count": 83, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "mean = 2\n", "plot_gammas(mean, [2, 5, 10])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "However, that doesn't mean that all gamma distribution behave the same way. In general, the higher the variance, the longer it takes to converge.\n", "\n", "With a gamma distribution, smaller means lead to higher variance. With `mean=0.2`, the sum of 10 values is still not normal." ] }, { "cell_type": "code", "execution_count": 84, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "mean = 0.2\n", "plot_gammas(mean, [2, 5, 10])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We have to crank `num` up to 100 before the convergence looks good." ] }, { "cell_type": "code", "execution_count": 85, "metadata": {}, "outputs": [ { "data": { "image/png": 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C+akOSzlIKhFkoGhc47vPf0S+UcdfbziWqXW5VWvd4XDsHhwu1IXhua8kSkhf8xwUqrIEY2Vb7za+u/S7dAY7Ob3hdBacvACrwZrqsJRDoBJBBvrV4q20DQf58Zm1TK0vTXU4YyoUCtHd3U1hYSE1Ngv88YzE4PB/3AONx6U6vJzgDrm5e9ndvGF/g6iMcsexd3DZ5MtSHZZyGFQiyDCaJnn6gy6OqzNzyTETUh3OmNpVRkMIwbgSPeLJS8HVCde9ppLAGHll2yvc9cFdjERHOLrkaL53wveYXDY51WEph0klggzz1tZB3MEYJzbbKCwsTHU4Y8rhcODz+ZjsXoJx4V2gN8O5d6skMEbe6HqDO967g0ZLI/MnzedzR30OndrKMyuoRJBBIjGNHy/cSE2BnguOasypKXnRaBS73U5pbICCZb+EpuPhc/dDWW61ilLlqc1PsWDFAmrNtfyw9YfMmTZHJYEsohJBBnnlo166nUHmn1hCbVVuLc3v7u5G0zSaNvwmUUX04oehKHcK6qWKJjVeanuJBSsWMKNwBt8e/22Oaj0KvT631qxkO5UIMoSUkvsWb6UqX8/pU6oxGHLnT+d2u3G7HEzZ/hi6nmVwzgKVBMbIT5f/lBe2vkCDtYGvN3ydmZNnYjSqHcOyTe6cTTLciu1OdriD3HR0MVUVZakOZ8xomkZPTw+NHc+Qv+kpmH4pzL4u1WHlhHZXOy9sfYHWwlb+u+m/mTxpMlarmh6ajVQiyBDPrOimyKznxKZ8iopya89ha8/bVGx6FKZeBJc+ojaVGSP/b+P/w6gzcn3t9YxrHpdzkxNyiUoEGUBKyfLtTqZXGqmrKs+ZQeJYLEbkg0eZuOYXUDEl0SWUI797Ku3w7eAH7/2AVQOrOL30dKbUT6GsLHdaoblIJYIMYHcF6feEOG98IaWlObKALBrE/7ef0Lj2IWRBNeK61yAvR373FNKkxu3v3s664XVcXHUxVzRdQV1dXarDUpJMJYIM8NyqHgCOaSgkPz8HisvFY2iPX0SxfTnBuhOwXvsUWHNn3+VU+mf3P/lw8EOuqruKz1V+jskTJ+dMCzSXqYnAac4bivK7t7cxq8rEjOYcqaOz5H/R2Zcz0HINxusWqiQwRgLRAHcuu5N6az2nF5/O+PHj1QyhHKESQZr7sMtFNC65eEo+Npst1eEkn7MD+d79eMuPQp7+w5yaJptqf1z/R9xhN1+u+TLjGsdRUFCQ6pCUMaISQRrTNMnv3t6GxSCYVJFHXl4ObLm47EGkzoB99veprMqRFlAaGAoM8eeP/0xrfitzaudQpV77nJLURCCEOEcIsUUI0S6EmL+XxxuFEEuEEGuEEOuEEP+RzHgyzf3/bGN5h5MvziykoSoHZm0MbEJ++DiumpMpGz9LlTAYI6FYiHtW3oM/6uey2stobm5OdUjKGEtau1sIoQceAOYBdmClEGKhlHLTHk/7AfCclPIhIcRUYBHQnKyYMs3rG/pprc5n3nhrbnQLvXUXmt5K/6ybaa3IrRIaqRLVolz+yuV0ejs5p+wczp1xriofkYOSecl1DNAupeyQUkaAPwMXfuI5Eti1OqoY6E1iPBllJBRl25CPI6stmIzG7O+v7VwKmxfiqD2V8qZW1RoYI0u6l9Dp7eTCigv51sxvqUVjOSqZ/211QM8e9+07j+3px8C1Qgg7idbAt/b2jYQQ1wshVgkhVg0NDSUj1rTz9tYhYppkepmguLg4u6fwBZzw7DVE82sYnnwtFao1MCbe6nmLW9++lTpLHZc2XEp9fX2qQ1JSJJmJYG9nLvmJ+1cBj0kp64H/AJ4QQnwqJinlw1LKOVLKOblykljT7cZs0DHBps/+bqHlD0LQRfuRP6B03EzVGhgDqwdWc/ObNzOhYAK3NN3C5AmT1euew5L5l7cDDXvcr+fTXT9fBZ4DkFIuAyxAeRJjyhgrtjuZUmnFqNdld22hsA9W/hFf/SlEKmao1sAYiGtxfrrsp9hMNm6svZEZTTNyY0aask/JTAQrgRYhxDghhAn4PLDwE8/pBs4AEEK0kkgEudH38xnCsTib+7xMLjVQUFCQ3Vdqb90FQRf25supqKhQA5Vj4I3uN9jm2cbnqz9PY0kj1dXVqQ5JSbGknWGklDHgJuB1YDOJ2UEbhRB3CiEu2Pm0W4GvCSE+Ap4Bviyl/GT3Uc7pcQaJaZLqPCguLk51OMmz+jFY9n8EGs8gUDqNysrKVEeU9ewjdm5/93ZqrbUcVXgUTU1N2T3+pByQpC7blFIuIjEIvOexH+3x+SbghGTGkIne3ppoFFXm67O3W6j7A3jl22i1s9k6/VbKysrUKuIkk1Ly4NoHiWgRbqi7gYaaBrW/gAKoonNp6a9rdlBXZGRaVV72/qO+ew/kVzAw70HiTr9ayZpk9hE7d7x3Bx8OfshZFWcxsXgiNTVqlzclQSWCNLOlf4T1OzxcPaOQEluWdgsNbYG2fyCPvYFBb5ji4mIsFkuqo8pqv1j5C7a4tvCNSd/gWOOxNDU1ZffYk3JQ1Dshzby6rhe9gNObLNk7PvD23WCw4Gz9ArFYTLUGkuxd+7u81fMW106+lrnmuZSXl6uFY8q/UYkgzbyxeZCp1fmUWPXZ+c9qXwUbXkAecz39fsjLy8vO3zONPLj2QWryazjJehJ6vV4tHFM+RSWCNPJht4vNfV5m15jJz8/PzsHTNU+CqYCRo24kFAqp1kCSvbfjPTY4NnBW7VnEgjHq6+uz832lHBaVCNLIW1uG0Ak4tcGQnVfJIS9sfAnGncKQJ4DBYMj+VdMptKhjEd9681s0FTZxnPk4CgoK1N7Dyl6pS4M0snK7k5piM4UmXXYmgrVPQ8hN9Oiv43a7qa6uVgOWSbJ6YDV3LL2DqWVT+fbEb6Mf0dPQ0LD/L1RykvovTBPdjgDLOhyc2FyEECI7q42ueRJsjQxZJwKochJJEowFue3t26gvqOe+E+5DP6KnvLxclZFQ9kklgjTxqze2YtQLTm1MjA9k3ZVy1/swsAF5xLUMDQ9TXFyMyWRKdVRZacGKBQwHh/nhcT/EO+hFr9dTV/fJwr+K8i9ZdrbJTIFIjNc29HHxEXVUmmPZ2S30/m+hsBp3y6XEYjHVGkiSTY5NvNT2El+a+iUmWSfh9Xqpra1VA8TKZ1KJIA28sXmQUFTjxHGJBJCViWBwM9QfzaAvjslkyt7SGSnkCXu4fvH15Bnz+PK0L2O327FYLCrpKvulEkEaWLxpgIpCM7MqDQghyM/PT3VIo8uzA1zbiZZNxufzUVFRoQqdJcEbXW/gCXu468S7iHljhMNhGhoa1Gut7JdKBGlg4w4PRzXa8Pt82Vl2eu3TAAxXnYgQgvJyteXEaAvHw/xh/R+oya9hbtVc+vr6sNlsquWlHJAsO+NknqGRMB3DfqbVFBIMBrOzW+jjV5F1cxiI2ygpKVH91UnwRtcb7PDt4KYjb2JwYBAppVpBrBwwlQhSbFmHA4AZVYkqo1mXCAY2Qd9aguPOJh6PqwVNSbB+aD0/eO8HlFnKOL3mdIaGhqioqMBsNqc6NCVDqESQYu+1DWE16mkuAiFE9s31Xv0Y6E30VZ2GyWTKvkSXYn2+Pm57+zZKLCU8cvYjDPQNoNPpVIlp5aCoRJBCmiZZsmWIM6dWEQ4Gsm/9QCwM6/5MfMr5uCM6ysvL1cDlKHtkwyP0+nu5++S7qTJU7V6xrbrflIORRWedzPNO2xBDI2HOnFJBIBDIvtXEH/4JQh7cDfMAVLfQKOv19bKoYxHzmuYxp3oOdrsdo9GoCvkpB00lghT6x6YBCs0GTmguREqZXYnANwhv/ATZcCy9eVMpKipSK4lHkZSS+1ffT0SL8J2jvoPb7cbv91NbW5tdrUplTKh3TAp1OwKMr8gnGgoAZNf6gcU/gsgI/lPvJBKNqdbAKIpqUW59+1Ze63yNyyddTkNhw+7FY+p1Vg6FSgQpIqWkfdDHuPJ8fD4fVqs1e/p1A0746BmYdTWDohK9Xq/KTY+i3675LYu7FnPBhAu4ZfYtDA8PEw6HqaurU2MwyiFRiSBFuhwB+r0hZjeV4Nu5kCxrbHwJgPiMK3G73ZSVlanuilEyHBzmiY1PcN748/jZiT9DL/T09fVRUFCgkq1yyNR/Z4q81z4MwOz6AjRNy65EsOpRKJ+Ms3AyUkrVXTGK/rDuD8RkjK9M/woAQ0NDRKNRamtrUxyZkslUIkiRpe3D1NmslJniANmTCPo+goENMPvLOFweLBZL9q2NSJFOTyfPb32eCyZcwKSSScTjcfr7+ykqKlLrM5TDohJBCsQ1ydL2YU6YWIbf78dkMmXPjJo3fwZ6E+FJn8Pv96vWwCj6zZrfYNAZ+OYR3wRgcHCQWCymWgPKYVOJIAVe+agXbyjGyZMq8Pv92TNbKBaG7e8kWgPhxMB3aWlpioPKDh87P+atnre4pOUSagtqicViDAwMYLPZsuf9o6SMSgQpsLLTSZ5Jz5mTyohEItnTLdSzAmJBGH8aTqeTwsLC7GnppNgvV/6SYnMx/znjPwEYGBggHo+r1oAyKlQiSIHNfV6m1xUTDGbZ+oH37gO9CV/FEYTDYdUtNEp6RnpY0b+Ca1qvodxaTjQaZXBwkJKSEqxWa6rDU7KASgRjTErJlv4RptYU4fP5sqfQnGcHbHsTjrwWhy+KTqdT0xlHyZObngTg7OazAejv70fTNNUaUEaNSgRjrH3Qhz8SZ3J14e7xgaxYBLTk54BAO/ZGXC4XNpsNvV6f6qgyXpe3i6c/fppLWi6hobCBSCTC0NAQZWVlWCyWVIenZImkJgIhxDlCiC1CiHYhxPx9POcKIcQmIcRGIcTTyYwnHfx9Qz8Ap04qJxAIZEe3kGMbrHsWjv4qHkO52ndgFL3V8xYA1027Dki0BgBVZloZVUmraSCE0AMPAPMAO7BSCLFQSrlpj+e0AN8HTpBSuoQQlcmKJ128sXmAoxptFBo0erOl0NxbC0CLwnE34nQ6MRqNal77KAhEA/xh/R+YUzWHpqImIpEIw8PDlJWVqU1nlFGVzBbBMUC7lLJDShkB/gxc+InnfA14QErpApBSDiYxnpQLRuJs6PVy/IRy/H4/kAUDxfEodCyBqRcRK27C4/FQUlKSHd1dKfbk5ifxhD3cfNTNCCFUa0BJmmQmgjqgZ4/79p3H9jQJmCSEWCqEWC6EOGdv30gIcb0QYpUQYtXQ0FCSwk2+jb0e4ppkVoMNn8+H2WzGaDSmOqzDs/wh8A9B6/m43W6klGrtwChoc7Xx2zW/5ejqozmi4oh/aw2oKbnKaEtmItjbJaH8xH0D0AKcClwF/FEI8ampJlLKh6WUc6SUcyoqKkY90LGytscNwKz64uxYSCYlfPRnqJgC0y/F6XRiNpsz//dKsZHICAtWLMBqsHLfKfep1oCSdMlMBHagYY/79UDvXp7zspQyKqXcDmwhkRiy0ppuN7XFFmwWHdFoNPNPmIObYXAjTL2QSDTKyMiIag2MggfXPsiK/hXcfOTN2Cw21RpQki6ZiWAl0CKEGCeEMAGfBxZ+4jl/BU4DEEKUk+gq6khiTCkTisZ5a8vg7rISkAXjA462xMfJ5+JyuQBVUmI0rOxfyZyqOVw79VpAzRRSki9piUBKGQNuAl4HNgPPSSk3CiHuFEJcsPNprwMOIcQmYAnwXSmlI1kxpdJbWwbxR+KcN7MGv9+fHQvJupaBzpAoOe10kpeXp+a2H6Ytzi1scW3hlPpTAFRrQBkTSd0SS0q5CFj0iWM/2uNzCdyy85bV3mkbptBiYO74Mra1t5GXl5fZM2vCI7D2aZh6ISFNRyAQoL6+PtVRZbxfrf4VNrONc8Yl5k2o1oAyFtTK4jHyYZeL6bXF6HUiOwaKt74OYQ8c/Z84nU5AdQsdLn/Uz5rBNZzZdCbV+dWqNaCMGZUIxoA/HOPj/hGOGVdKMBhESpn5iWDJz8Fggdojd1cazfipsCm2pGcJgViACyYkek4HBgYAqK6uTmVYSg5QiWAMbO7zAjBz57RRyPCBYncPOLfBcTfgj2iEw2HVGjhMUkpe7XgVm9nGzPKZRKNRhoaGKC0tVauIlaRTiWAMtA/6AGipTBSaMxgMmf3P3bjB9tYAACAASURBVL0s8XHK53C5XAghVKXRw/Ta9tdYumMpX572ZfQ6PQMDA0gp1diAMiZUIhgDH9k9FFoM1JVYs2N8YO3TUFCFrJqG0+mkqKgIgyGp8w6y3rNbnqUqr4qrW68mFoup1oAyplQiGAMOX5jaYitSixMKhTK70FzAmdiO8ohr8IViRKNR1S10mDxhD2uH1nLhxAuxGqwMDAygaZpqDShjRiWCJNM0ycZeL3UlVgKBLNiRbM0TIOMw9UJcLhc6nY7i4uJUR5XRfvfR79Ckxin1pxCLxXbvPqbWZChj5TMTgRDisT0+/1LSo8lCPa4AO9xBzmit3D1QnLELybQ4vHMvVM9EVs/E5XJRXFysNqA5DOF4mGe3PMvcmrnMKJ/B4OCgag0oY25/LYJZe3z+7WQGkq1WdyVKL8yss+H3+7FYLJl74nznnsTagbk3MeLzEYvFVLfQYfr79r8T1aJcOflKNE1jcHAQm82m9iJWxtT+EsEnq4UqB+n9bQ5seUam1RZl9kDxwCZ46+fQcOzuSqN6vZ6ioqJUR5axfBEfj218jLqCOk5rPI3BwUHi8bhqDShjbn9TPeqFEL8hUVJ61+e7SSlvTlpkWWJtj5vZjSVEoxFisVjmJoKPX018vPxxNKHD7XZjs9nQ6dQw06G6a8VddHg6uPeUe5GaZHBwkOLi4sztOlQy1v4SwXf3+HxVMgPJRv5wjPZBH5/bWWgOMnigeONL0DgXimrwut3E43HVLXQYOj2dvNrxKldOvpIzm86kv7+fWCymWgNKSnxmIpBSPj5WgWSjj+yJjWh2rSjW6XSZ2ffbuRQGN8G5dwPgdDoxGAxqX+LDsLhrMZrUuH7m9WiaxsDAAIWFhZl7oaBktP2264UQXxJCfCiE8O+8rRJCfHEsgst0a7oTiWB2Yyl+vz9zK44uewAKquHIa4nH42pf4sMUjAV5rfM1mouaKbeWMzw8rFoDSkrtb/roF4HvALcCtST2HP5v4NsqGezfRz1u6mxWiqwGAoFAZl7tSQl9a6H5BDDl4/F40DSNkpKSVEeWse5bdR9trja+Mv0raJpGf38/BQUFqoWlpMz+WgQ3AhdLKZdIKT1SSreU8k3g0p2PKfugaZK3tw4xtbYosyuOuraDdwc0HQ8kuoWMRmNmr45OoVAsxN+2/41zx53LxS0X43A4iEajqjWgpNT+EkGRlLLzkwd3HlPzBj/DwEiIcEzjpJbyzB4o3vZm4mPj8cRiMbxeL6Wlpapb6BAt3bGUkcgIF0+8GCkl/f395Ofnq2m4SkrtLxEED/GxnNflSJSTGF9esLviaEZuLtK1DIrqoGoqbrcbKaXqFjoM7+54lwJjAXOq5+B0OolEIqo1oKTc/qaPtgoh1u3luADGJyGerNHnSeTJGpsF/+BAZrYGAHashtojAXC5XJjN5sz9XVLsn13/ZNH2RZxUdxIGYaCvrw+r1apqNSkpt79EMAuoAno+cbwJ6E1KRFmifdCHQSeoKTKzuTuUmXPu3d2JMYI51xGNRvF6vWq3rEMUiAa4/b3bGV88nvnHzMflchEOhxk/Xl1PKam3v66hXwFeKWXXnjcgsPMxZR829XqZUFFALJxoGWTkVfTW1xMfJ87D7U5Mhc3IhJYGnt/6PIFYgPnHzKfcWk5fXx8Wi0Vt6KOkhf0lgmYp5ae6hqSUq4DmpESUBaSUrO5yZf7WlF3vQ145VLbidDqxWCyZuSAuxUKxEH9c/0eOrDySWRWzcLvdhEIhampq1KC7khb2lwg+qyC6OiPsgzsQxRuKMaWmKHMrjkZDsPXv0Ho+kWgUn8+nWgOHaOG2hbjDbr4+8+sA9PX1YTab1aC7kjb2lwhWCiG+9smDQoivAquTE1Lm63ImZgzV2TJ4a8rtb0M0AK2fw+l0Aqpb6FAt2r6ISmslx9cej8fjIRgMqtaAklb2N1j8HeAlIcQ1/OvEPwcwARcnM7BMtnVgBICKfD0xZ4ZWHP34b2AqhOaTcLV1kJ+fr/bPPQSesIfVA6u5pvUahBC7WwMqqSrpZH9F5waA44UQpwHTdx7+287Vxco+/G1dH2X5JuoLBHZnBo4PSJkYKJ54OqGYJBAIUF9fn+qoMtLirsUAnNN8Dh6Ph0AgQFNTk2oNKGllfy0CAKSUS4AlSY4lK/jCMZZtc/DFuU1EQsHMrDg63Aa+fphwuuoWOgxSSp75+BlaSlqYVTGLLVu2YDKZKCsrS3VoivJv1K4io2zFdgeRuMbxE8syt+Loe78CvQnGnYzT6aSwsBCj0ZjqqDLOIxseYatrKxdNuIiRkRH8fj/V1dWZ935Qsp5KBKNsVWdij+Jjmkszs+JoeAQ2vACzrsJvriIcDqvWwCEIxUI8sekJppRO4erWq+nr68NoNKrWgJKWVCIYZSu2O5lRV4yIRzKz4mjPCohHYPK5uFwuhBBq0dMhuGfVPThDTuYfM5+gP4jP56O6ulpt7amkJfWuHEWaJtnc5+WoRlvmLiT7+FXQGZENx+F0OikqKsJgOKChJGWnfn8/L7e/zLnjzmV21Wx6e3sxGo2Ul5enOjRF2aukJgIhxDlCiC1CiHYhxPzPeN5lQggphJiTzHiSbYc7iD8S372QzGg0ZlbFUf8wfPgEzLgcX9xANBpV3UIHSZMa1y++Hp3Q8c0jvonX61WtASXtJe2dKYTQAw8A5wJTgauEEFP38rxC4Gbgg2TFMlY+7E6MD7TWFOHz+TJv85ZNL4MWheNvwul0otPpVLfQQXrH/g7bPduZf8x8moqado8NqNaAks6SeYlyDNAupeyQUkaAPwMX7uV5PwXuBkJJjGVMrOx0YjXqaSm3EolEMqtbSEpY/f/A1ohWPgWXy4XNZlNXsQfplW2vUGwu5rzx5+1uDdTU1KjXUUlryXx31vHv5avtO4/tJoQ4EmiQUr76Wd9ICHG9EGKVEGLV0NDQ6Ec6SjqG/NSXWIlmYsXRvrXQvx7mfguP10s8HlczXA6SN+LlrZ63OLX+VEx60+6xAfU6KukumYlgb5Ol5e4HhdCRKGV96/6+kZTyYSnlHCnlnIqKilEMcfR4Q1He3+bgnOnV+P1+hBDk5eWlOqwDt/BmMBftri1kNBrVZuoHaXnvciJahLObz8br9eL3+1VrQMkIyXyH2oGGPe7X8++b2RSSKFvxlhCiEzgOWJipA8Yf9STq9c9uKsHn85GXl5c5JwCPPdEaOOFmYnmVeDweSkpK1MKng/TC1hcotZRyXO1x9Pb2qlXESsZI5plqJdAihBgnhDABnwcW7npQSumRUpZLKZullM3AcuCCnXsdZJx1dg8A02uLMm8h2ZbXAAktZ+FyuZBSqhPYQbKP2FnWt4zLJl1G0BfcvYo4Yy4GlJyWtHeplDIG3AS8DmwGnpNSbhRC3CmEuCBZPzdV2gZGqLNZydNraJqWWYlg/QtQOh6qZuzegCajurXSwLqhxP5NZzWdtbs1oGYKKZkiqSuFpJSLgEWfOPajfTz31GTGkmyb+rxMqCzA5/MBZM7UUb8Dej6A024nvHMDmtra2lRHlVF8ER8Pr3sYq8GKTdqw++00NjaqrjUlY6h26ygYHAmxdcDH8RPKMm8hWf86QEL90arS6CGIa3H++53/psPTwV0n3oVjwIHZbFatASWjqEQwCrYNJspJzKgrzryFZN3LQeig7iicTicFBQVqA5qDsLxvOe/ueJfvzP4ORxYeSTAYpLa2VrUGlIyiEsEo2NibGChuKDYRiUQyJxFoGnz0DFTPxB83EAqF1CDxQfqg7wOMOiNXT7ma3t5erFar2otYyTgqEYyCjb1eqorMFOhjQAaND3QvA3cXzL0Jh8OBTqdTJ7GDEIgGWLhtIfWF9fjcPsLhsGoNKBlJJYJRsLHXw7TaYvx+f2btSLb+OdCb0SacgdPpxGazodfrUx1VxljZvxJHyMF1066jt7eX/Px8VZtJyUgqERymQCRGlyPAhIp8fD4f+fn5mXFFqGmw7U0YfwruMKqkxCF4se1FDMLA7ILZRKNR6urq9v9FipKGVCI4TEvbHYRjGie3lBMIBDKnW2jHKnB3w/TLcDgcmEwmVVLiAAVjQX6y7Ce82fMm540/D9egi8LCQvX6KRlLJYLDtN7uRq8TTC5L7OmbMQvJVjwMBguRplPwer2UlZVlRksmDdyz8h5e2PoC1027jq+P+zqxWEy1BpSMphLBYdo64KOpNI/YzoqjGdEiCLpg6+sw/VKcO4t/q26hA+OL+Hih7QVOaziNb836FsODw9hstsy5AFCUvVCJ4DBtH/YzvqIAv9+P1WrNjMHWv98OER/M+QrDw8Nq7cBB+EfXP9CkxhemfoG+vj40TVOtASXjqURwGAKRGB3DPupslsxZSBbxw/rnYepF+GxTCIfDqjVwgLwRL3evvJvmomZai1oZGhqioqICi8WS6tAU5bCoXckPQ8eQn2hcMrMmH01zZsZg4brnEttRHvt1hoeH1dqBg/DEpifwR/08ctYjDPQNoNPpqKmpSXVYinLYVIvgMHQ7AwBUWBL77aR9iyAehQ8fh7KJxGvn4HK5KC0tzYzurBSTUrK8dzkTbRNpsjThdruprq7GaDSmOjRFOWwqERyGXYmgSB/BYrGk/0lh6+vQuwaO/QYOpxNN01RxtAP03o73WDu0lktaLsFut2M0Gqmqqkp1WIoyKlQiOAxdDj+l+SZkJJgZ3UKbF4KlGI78AsPDw+Tl5anZLgdo4baFGHVG5lXMw+/3U1dXpzadUbKGeicfhk19IzSWWNA0Lf27hWIRaH8DJpyBPxInGAyq1sABimtx3t3xLmc1ncVQ/xBWq1WV6layikoEh8jlj/BRj5vWykRdobRvEXQthYADZlzO0NAQOp1OncwO0EdDH+GP+pmWP41IJEJ9fb1afKdkFZUIDtF2R2IPgqllBsxmc/qPDwxuAiBeO1sNEh+Et3ve5qY3b6LcUk6T1kRxcTFFRUWpDktRRpVKBIeofTCxJWWZKZb+rQGA3rWQV44jJNQg8QEKxoLc9vZtGISB/53xvxToC2hoaEh1WIoy6lQiOETr7G7yTXrKrRnQLdS3LlFyummuGiQ+CC+2vUgoHuKHc36IJWihurparcBWspJKBIdond3D5EoreiHSPxGs/CMYLPhOuZNgMEhFRUWqI0p7A/4B7l11LzPKZ1AZqsRkMlFdXZ3qsBQlKVQiOAT+cIyNvV6mlJmwWq3pPT4QdCVWE8+8ggG/xGAwqEHiA/Bqx6tEtSi3Tr2VWDhGfX29mi6qZC31zj4Ea7rdxDXJhGLSf+Bw25sQCxKZfhVut5vy8nJ1QtuPfn8/v1/3e8YVjUPv0VNYWKjKcChZTZ0RDsHKTic6AZNKDenfLdT+T9CbGNQnujVUt9D+PbflOUKxEN9u+TbxeFwNECtZTyWCQ7DO7mZcqYV8kz69E0EkAOufR1bPYNjlpaSkBJPJlOqo0lpUi/Jqx6scU3UMtrCNysrKzNmDWlEOkUoEh6DPE6IyT0dBQUF6d7OsexbiEbzTv0Q8HqeysjLVEaW9v2//O33+Po4vOB6TyURtbW2qQ1KUpEvjs1h6klJidwUpNqX5tNGQB974H6StiZ6CI8jLy0v/Mhgp5o14eXzj41RYKphmmUZjY6NadKfkBJUIDtKwL4IvHKOuUJ/eA8VtiyHkIXDKjwlHYqpS5gH44Xs/ZItrC+eUnkNlWSXFxcWpDklRxoTamOYg2V2J0tNVhUby8vJSHM1n2PQy5JVjt0zBFIurWS/70efr482eN7m07lLOrjhbDRArOUW1CA7S5j4vABOrbelbeCzghK1/JzLlQnyBIFVVVekba5p4ZMMjABxlPYqGhgYMBnWNpOSOpL7bhRDnAL8G9MAfpZQLPvH4LcB/AjFgCPiKlLIrmTEdrsUb+ygwCqY1pvE0zI0vQTxCf9VpGAwGVVdoP1b2r+TZLc8y1zaX1spWteAuCaLRKHa7nVAolOpQsp7FYqG+vv6gFromLREIIfTAA8A8wA6sFEIslFJu2uNpa4A5UsqAEOIG4G7gymTFdLjCsTjvtTs5ts5MeWkad7V89Axa+RSG9DXUVlam98ymFAtEA9z+7u0UGAq4pvYampqaUh1SVrLb7RQWFtLc3Kxap0kkpcThcGC32xk3btwBf10yzxDHAO1Syg4pZQT4M3Dhnk+QUi6RUgZ23l0O1CcxnsO2bdBPVJOcMsGWvrNJHNvAvhJX4znoDQY1ZXQ/7l11LwOBAW6sv5GpzVPVOoskCYVClJWVqSSQZEIIysrKDrrllcxEUAf07HHfvvPYvnwVeC2J8Ry29T0OAGY2laU4ks+w40MA+gunU1FRkb4JKw1sc2/jua3PcXb52Rxff7xadZ1kKgmMjUN5nZM5RrC3aORenyjEtcAc4JR9PH49cD1AY2PjaMV30NZ3OzHqYFpjGl9l969D6gxEChpUa2A/FrYvRCC4sPpC1SWk5LRktgjswJ5z8OqB3k8+SQhxJnAHcIGUMry3bySlfFhKOUdKOSeVV21dDh9VBQYK8tN32qi2/R18tlbKq+vSuypqinnCHp7a/BQT8yYys2WmmiWkjLmenh5OO+00WltbmTZtGr/+9a93P+Z0Opk3bx4tLS3MmzcPl8uV1FiSmQhWAi1CiHFCCBPweWDhnk8QQhwJ/J5EEhhMYiyHLRaL0e8NU1VkSXUo+xZwIvrX4y+fpWrn78fdy+8mrIX5UsuX0nthoJK1DAYD9957L5s3b2b58uU88MADbNqUmEuzYMECzjjjDNra2jjjjDNYsGDBfr7bYcaSrG8spYwJIW4CXicxffRRKeVGIcSdwCop5ULgl0AB8PzOfq1uKeUFyYrpcHT2DdHhivL5Cenb3RJe8xxmGUc3/WLVGvgMDr+Df3T/g5lFMzl/5vmpDifn/OSVjWzq9Y7q95xaW8T/nD9tn493dnZy7rnncuKJJ/L+++9TV1fHyy+/jNVq5dRTT+Wee+5hzpw5DA8PM2fOHDo7O3nsscf461//SjweZ8OGDdx6661EIhGeeOIJzGYzixYtOqypxjU1NdTU1ACJcjWtra3s2LGDqVOn8vLLL/PWW28B8KUvfYlTTz2VX/ziF4f8s/YnqfMKpZSLpJSTpJQTpJQ/23nsRzuTAFLKM6WUVVLKI3be0jIJAKzdPkhcwlkzPmu8O4XiMcSy3xIqaKRs6qmpjiZtSSm56927CGkhvj/3+2pqbQ5pa2vjm9/8Jhs3bsRms/GXv/xlv1+zYcMGnn76aVasWMEdd9xBXl4ea9asYe7cufzpT3/61POfeuopjjjiiE/dLrvsss/8OZ2dnaxZs4Zjjz0WgIGBgd1JoqamhsHB5HaYqI7RAxCLxegaHgGgoSQ9SxKH3vk1Fp8d7yl3YlH93fv0hxV/4PWB1zmh6gSmV09PdTg56bOu3JNp3LhxHHHEEQDMnj2bzs7O/X7NaaedRmFhIYWFhRQXF3P++YkW5IwZM1i3bt2nnn/NNddwzTXXHFRcPp+PSy+9lPvvvz9l3ZTqjHEA3G43GwcjFJj11KVjIgh5ML/zM3zlR1Bw0o2pjiZtLWlbwoMfP8js0tn831n/l+pwlDFmNpt3f67X6wkGg0Cir17TNIBPzb/f82t0Ot3u+zqdjlgs9qmf8dRTT/HLX/7yU8cnTpzICy+88Knj0WiUSy+9lGuuuYZLLrlk9/Gqqir6+vqoqamhr68v6TMAVSI4AC6Xi3WDEY4bX4bZkH7z8v1L/0C+jKMddxM6gxob2JtAIMB9a+6j2FTMb876DQadeusrCc3NzaxevZpjjjlmryfrg3EwLQIpJV/96ldpbW3llltu+bfHLrjgAh5//HHmz5/P448/zoUXXriP7zI6VAfpfsRiMQadboYDcY5sTL+yEvFoBOOq3xMsmULhkRelOpy0FIvFWLJhCZ3BTq6cfCVFZjVLSPmX2267jYceeojjjz+e4eHhMfu5S5cu5YknnuDNN9/cPZawaNEiAObPn8/ixYtpaWlh8eLFzJ8/P6mxCCn3usYrbc2ZM0euWrVqzH7ewMAAb37UwfffdPLA1Udx3syaMfvZB2JoxYtULLqO0PkPYZl9darDSTtSStra2vivNf+FPWTnb5f8jfrCtK5kkpU2b95Ma2trqsPIGXt7vYUQq6WUc/b2fNUi2I/h4WFW9McxGXScODG9qngGg0HY+CJSb8IyI7lNx0zV3d3Nk9uepDvUzfeO+Z5KAoqyFyoRfAa/308oFOL9niCzG0sozkuv/ve+De9S3r0IOf1yMOWnOpy009vby8ttL/PS4Et8bvznuGrKVakOSVHSkkoEn2F4eBh3WDIwEuHElvRqDTgcDvI3PwtSQ3fGD1IdTtoZGhrig44PeKz3MaaWTeXO4+9URc8UZR9UItiHeDyO0+mkK5BoBcydkD4VR6PRKPaeHkr734P6o6GoNtUhpRWXy8XytuXc33M/heZCHjjjAYz69GrNKUo6UYlgH1wuF5qmsc0jMel1TKtNn5kmnZ2dWIc/whjoRxx5barDSSsjIyOs3rqaX3f/GlfExYKTFlBuTa/WnKKkG5UI9mFwcBCDycLfNw1xRmtl2qwfGBwcxOv1Uu9bBzojTL9k/1+UI7xeL21tbTy641GGIkM8dOZDzK2dm+qwFCXtqVU1e+HxeAgGg3REinD4I1xxdMP+v2gMhEIhduzYQVFREXn2d6D5RDAXpjqstODxeHh347s82f8kG0c2ctWUqzih7oRUh6Uon6m5uZnCwkL0ej0Gg4FdU+OdTidXXnklnZ2dNDc389xzz1FSkrx1TKpFsBcDAwMYjUZW2AMUmg2clAbTRqWUbN++HSEEzRYvDG+FSeekOqy04HK5eGzVY3y/7ftsGtnEjbNu5LtHfzfVYSnKAVmyZAlr165lz/VRWVOGOlP5/X5GRkaoravj9Rc/Yu6EMgz61OfLnp4eAoEA48ePx7jyXhA61S1E4sppQ/sGHrU/yozyGfz8xJ/TXNyc6rCUz/LafOhfP7rfs3oGnLvvk2U6lqH+LFlVhjoTDQwMoNfr6QkY8IZinDM99Ru8DA0NMTQ0RFVVFSXFxdC1DKpnQkH67o0wFgYGBtjWsY1fdv0SDY1bZt+ikoCyT+lYhloIwVlnncXs2bN5+OGHdx9XZahTKBAI4HK5qK6u5qGVfViNes5orUppTCMjI/T09FBUVERdbS28+VPYsQrOvTulcaWSpml0d3fjcDgY1A/SGejkazO+xpzqva6eV9LNZ1y5J1M6lqFeunQptbW1DA4OMm/ePKZMmcLJJ598wF8/WlSLYA87duxAr9dTWVnJW1uGOGFiGcXW1M0/D4fDdHR0YDabGT9+POK9++C9++CoL8Ix16csrlSKRqNs3boVh8OBJ8/Doz2PYjVY+eLUL6Y6NCXNfbIM9a4y0qNdhvpgWgS1tYk1QJWVlVx88cWsWLEC+FcZamBMylCrRLCT1+vF6/VSU1PDNkcQuyvI6VNS1xqIRqO0t7cjpWTChAno+9YkWgMTz4TzfwM5uEo2EAiwefNmgsEgAVuAW1feSru7nduPvR2bxZbq8JQMtasMNTAqZajXrl37qdvevu+u8chdn//jH/9g+vTEZkm7ylADY1KGWnUNkZiRY7fbMZvNVFZW8td3OgA4bUpFSuKJxWJs3bqVSCTCxIkTseji8NTlYC2BCx/IuSQgpWRwcJAdO3ZgNBppmtDEF974AkXmIp76j6dUITnlsNx2221cccUVPPHEE5x++ulj9nMHBga4+OKLgcT//NVXX8055yRmAs6fP58rrriCRx55hMbGRp5//vmkxqLKUJNYpNXT08P48eMpKSnhC498wIA3xD/+65RR/TkHYlcSCIVCtLS0UJifDw8eB8Nb4KKH4IjcKjUdiUTo7OxkZGSE4uJimpqa+PEHP2bhtoUsOGkB540/L9UhKgdAlaEeWwdbhjrnWwR7LtIqKSmh3xPigw4nVxw99leZsViMtrY2QqEQEydOpLCwELb8PZEETvgOzMqt6pkOh4Oenh6klDQ1NVFSWsJv1vyGhdsWctWUq1QSUJRRktOJQEpJZ2cnQgiampoAeG1DH5G4xhVzxnY1cTAYpL29nWg0yoQJExKbWMdj8Np3E11CJ9+WM11CoVAIu92Ox+OhoKCA5uZmzGYzD330EI9ueJTLJl3G947+XqrDVJSskdOJYGBgAL/fz7hx4zCZTEgp+fOKHupLrMyoKx6zOLxeLx0dHQghmDx5Mvn5O/cWWP4AuLvh8sdzopREPB6nr6+PwcFBhBDU19dTWVmJEIIB/wDPbH6GWRWz+NFxP1IlpRVlFOVsIvB4POzYsYOSkpLdqwPX7/CwZWCEH5zXOiYnml2DoHa7HavVysSJEzGZTIkHh9vhzf+F2iOh9YKkx5JKUkqGh4fp7e0lFotRVlZGXV0dRqORPl8fL297mSc3P4kv4mP+MfNVElCUUZaTiSAYDNLR0UFeXh7Nzc27jz/9QTdmg25M9iXecxDUZrPR3NyMXr+zwqnHDs9cCcY8OP/XoMvOWb6apuFwOOjv7ycSiVBQUEBDQwN5eXn0+fr42Ts/4x37O0gkx1YfyzdmfYPp5dNTHbaiZJ2cSwThcJi2tjb0ej0TJkxAt/Mk6/n/7d1/cFX1mcfx90Ny8/sXITdKufyyAcNup1C0rLqWtZ2yo6wL2xlWYVaFlR1Wd3VQd6ZgO9vFznQGVretM+7YxqVYZlhZRqpSigKOshSZ5Yf80AiYIALekBACCc29SZMb8uwf5ySE5CYSkptzkvu8Zu7k5uTk5pPvJPe553zPfb7NMd49XsudXx3D2PzMhP18Ve2cBAWYOHEiRUVdmtrVnYR190HLH+DhN2Ds9IRl8cqVK1e4cOEC58+fp62tjezsbMaPH09BgfNegA+qPuDJ954k1h5j8Z8sZmHpQrtE1JgESqpCWHIAzAAADMpJREFU0NTURGVlJQBTpky5ehoG2HnsPHWRFv7pnpKE/fzGxkbC4TBNTU3XTIJ2UoVt/wJtLbDkdxAaOS0TVJVIJMLFixc7F/3Jy8vj5ptvJjc3l7b2Nrad2kZFfQXrj61nYt5EVn9rNbcW3up1dGMS5tFHH2Xr1q0UFxdTXl7eub23NtSqyvLly9m2bRtZWVm8+uqrzJw5c8A5RuY5hzgikQgVFRWdE7JZWVnXfH3TQWeS+LaJg9/zu6mpiZMnT1JRUUFbWxuTJk1i6tSpV4uAKlQdgg0L4NQuuH3JiCkCLS0tVFdXU15eTkVFBfX19RQWFjJt2jTnfRK5udREa1i2cxkrfr+CteVrmZg3kbI5ZVYEzIi3ZMkS3nnnnR7be2tD/fbbb1NZWUllZSVlZWU8/vjjg5IjaY4IWltbCQQCPY4EGv8Y4wdvlLP/80usvK+UlFGDMxGpqjQ0NFBbW0skEiElJYVx48ZRXFzceToKgPCH8PrfQ8MZQOAbD8N3/nVQMnih45X/5cuXuXz5cmfvltzcXMaNG0dBQcE1v39FfQXP7HqG6kg1d33lLl74ixfITRv5V0glszX713Di0olBfczSwlJWzOr9kmK/tqGePXt23OZ3vbWhfuutt3jkkUcQEe644w4aGhqorq7u7FR6o5KmEBQWFjJ69OgeV5y8+G4lvz16jiV3TWLxnZMG9DNUlWg0Sn19PfX19cRiMdLT0wmFQhQVFV2dDK49AcfehM93w5kPIOdmZ1K49K8he8yAMgy1jt85Go0SiURobGzkypUriAi5ubkEg0EKCgquKb4d9p7byw/3/JBoLMov5/zSuoeahKqsrOS1117jlVde4YEHHmDz5s089FDfa36Xl5dz+PDhzjd5rlmzhsOHD/P000+zfv16nnrqqWv237BhA88//3yPxykpKelXH6Pe2lBXVVUxfvzV9ziFQiGqqqqsEPRH9yJwsraRdXtPM2/6V1g1708H9Ni1tbXU1NQQi8UQEfLz8ykqKiIvL8/5uWf/Dyq2Ox/P7gUEgqVw9zPwzaWQ7//J0Pb2dpqbm52mb01NNDc3E41G6WhTkp6eTkFBAfn5+eTl5V0tfF180fgFO07v4Pil42w/vZ3izGLK5pQxo3jGUP86xiN9vXJPJD+2oe6veC2BBuNy6oQWAhG5F3gRSAH+S1VXd/t6OrAeuA24CDyoqqcTmUlVOX2xie2f1PDiu5Wkp47i2bmlA35cESE7O5vRo0eTn59/9Unwwqew80dQ8Q6MSoXiaTD7+3D7o5CX+MtUb0RrayvRaJSWlpZrbq2trZ37jBo1iszMTILBIDk5OeTk5BAI9GzZHWuPcaT2CMcuHmNP1R4O1hykTdvIS8tjwdQFPDvrWdJSeh4tGDPYurehbm5uBga/DfVgHBF0tKEeO3bsNW2oQ6FQ5xWHAOFwuLOV9UAkrBCISArwn8AcIAwcEJEtqnqsy25LgXpVLRGRhcAa4MFEZVJVVmz+iE0HwwBMH1/Aj+6fNiiXiwaDQYJjCuHcETi01Zn0bTgLTXWQngffXeWsIZCWPeCflWj19fWEw84Ypaamkp6eTk5ODhkZGWRmZpKWnkZ7Sjt1zXXUNNdwof4CF85doLapllOXTxFuDBONRYnGojS1NXU+bklBCQumLuDBWx+kZHTirs4ypj862lDPmjVrUNpQD8YRQUcb6pUrV17ThnrevHm89NJLLFy4kH379pGfnz/g00KQ2COCWcBJVT0FICIbgflA10IwH1jl3n8deElERBPQEnXj/rO8sONT6iKt3BLM5hcP3caU4pzBe5fqnp85tz9edtYTnnAXTLsf8kLOQjK53q501h97G/ay9sxa2rSNWHuMtvY2YlditLa3EmuP0a7tcb8vIyWDUG6I0sJSsgPZZAWyyA5kU1JQwvTgdG7KusneFWx8x6s21ACLFi1i165d1NXVEQqFeO6551i6dGmvbajnzp3Ltm3bKCkpISsri3Xr1g1KjoS1oRaRBcC9qvoP7ucPA3+mqk902afc3Sfsfv6Zu09dt8daBiwDmDBhwm1nzpzpd573T9Sy5eg57rxlDH/19bFkpw9yDTy6EU7vgVvucW7ZRX3v72O7w7vZ8tkWAqMCBEYFSEtJ67yfOiqVQEqAjJQMijKLCGYFKc4sJpgVJCcwiIXVjCjWhnpo+akNdbxnhO5V53r2QVXLgDJw1iO4kTDfLi3m26UJXO5t+kLnNgLMDs1mdmjo1001xngjkW8oCwNdezmHgHO97SMiqUA+cCmBmYwxxnSTyEJwAJgiIpNFJA1YCGzpts8WYLF7fwHwXiLmB4wx3rN/7aFxI+OcsEKgqm3AE8B24DiwSVU/EZEfi0hHX+W1wBgROQk8A6xMVB5jjHcyMjK4ePGiFYME62hqmZGR0a/vszWLjTEJF4vFCIfDPa7TN4MvIyODUCjU4309tmaxMcZTgUCAyZMnex3D9CJpuo8aY4yJzwqBMcYkOSsExhiT5IbdZLGIXAD689biIqDuS/fy3nDJCZY1EYZLThg+WYdLThiarBNVNRjvC8OuEPSXiBzsbabcT4ZLTrCsiTBccsLwyTpccoL3We3UkDHGJDkrBMYYk+SSoRCUeR3gOg2XnGBZE2G45IThk3W45ASPs474OQJjjDF9S4YjAmOMMX2wQmCMMUluxBYCEblXRD4VkZMi4uuupiJyWkQ+FpEjIuKrjnoi8isRqXVXk+vYVigiO0Wk0v042suMbqZ4OVeJSJU7rkdEZK6XGTuIyHgReV9EjovIJyKy3N3uq3HtI6fvxlVEMkRkv4gcdbM+526fLCL73DH9H7clvh9zvioin3cZ0xlDmmskzhGISApQAczBWfzmALBIVY/1+Y0eEZHTwO3dl+j0AxGZDUSA9ar6NXfbvwOXVHW1W2RHq+oKH+ZcBURU9QUvs3UnImOBsap6SERygQ+BvwGW4KNx7SPnA/hsXMVZIzVbVSMiEgD2AMtx2tv/RlU3isgvgKOq+rIPcz4GbFXV173INVKPCGYBJ1X1lKq2AhuB+R5nGpZUdTc9V42bD/zavf9rnCcHT/WS05dUtVpVD7n3G3HW6xiHz8a1j5y+o46I+2nAvSnwHaDjydUPY9pbTk+N1EIwDviiy+dhfPoH7FJgh4h8KCLLvA5zHW5S1WpwniyABC4GPWBPiMhH7qkjz09hdScik4BvAPvw8bh2ywk+HFcRSRGRI0AtsBP4DGhwF8kCnzwPdM+pqh1j+hN3TH8mIulDmWmkFgKJs83zqtuHP1fVmcB9wD+7pznMwL0MfBWYAVQD/+FtnGuJSA6wGXhKVf/gdZ7exMnpy3FV1SuqOgNnffRZwLR4uw1tqjgBuuUUka8BzwKlwDeBQmBITwmO1EIQBsZ3+TwEnPMoy5dS1XPux1rgDZw/Yj87754/7jiPXOtxnrhU9bz7T9cOvIKPxtU9P7wZ2KCqv3E3+25c4+X087gCqGoDsAu4AygQkY4FuHz1PNAl573uaThV1RZgHUM8piO1EBwAprhXDKQBC4EtHmeKS0Sy3Yk4RCQb+EugvO/v8twWYLF7fzHwlodZetXxpOr6Hj4ZV3fCcC1wXFV/2uVLvhrX3nL6cVxFJCgiBe79TOC7OHMa7wML3N38MKbxcp7o8gJAcOYxhnRMR+RVQwDuJW0/B1KAX6nqTzyOFJeI3IJzFADO0qH/7aesIvIacA9Om9zzwL8BbwKbgAnAWeBvVdXTidpect6Dc/pCgdPAP3acg/eSiNwN/B74GGh3N/8A5/y7b8a1j5yL8Nm4isjXcSaDU3Be4G5S1R+7/18bcU63HAYecl91+y3ne0AQ57T2EeCxLpPKic81UguBMcaY6zNSTw0ZY4y5TlYIjDEmyVkhMMaYJGeFwBhjkpwVAmOMSXJWCIzphYiM6dINsqZbx80eXSzd7qGPXcfjpopIQ2JSG9N/dvmoMdfhejqZikgJ8LrbPqCvx0oF6lS1YHBTGnNj7IjAmBsgIt8XkXL39qS7eTVwq3vEsFpE8kTkPRE55DYTu9/LzMb0JvXLdzHGdCUis4C/w+kHkwLsF5H/BVYCJR1HBG6fnvmq2igixcAHwFaPYhvTKzsiMKb/vgVsVtUmt0//m8DdcfYTYI2IfATsAMaLSNEQ5jTmutgRgTH9F6/NeTyPAPnATFVtE5EwkJG4WMbcGDsiMKb/dgPfE5FMt1f/fJzmbI1Abpf98oFatwjMwQeLohgTjx0RGNNPqrrf7XZ6wN30sqp+DCAiB0XkY+B3wE+B34rIQeAQUOlJYGO+hF0+aowxSc5ODRljTJKzQmCMMUnOCoExxiQ5KwTGGJPkrBAYY0ySs0JgjDFJzgqBMcYkuf8HI9td6whGE78AAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "mean = 0.2\n", "plot_gammas(mean, [20, 50, 100])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "With `mean=0.02`, we have to add up 1000 values before the distribution looks normal." ] }, { "cell_type": "code", "execution_count": 87, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "mean = 0.02\n", "plot_gammas(mean, [200, 500, 1000])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Pareto distributions\n", "\n", "The gamma distributions in the previous section have higher variance that the uniform distribution we started with, so we have to add up more values to get the distribution of the sum to look normal.\n", "\n", "The Pareto distribution is even more extreme. Depending on the parameter, `alpha`, the variance can be large, very large, or infinite.\n", "\n", "Here's a function that generates the sum of values from a Pareto distribution with a given parameter." ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [], "source": [ "def sum_of_paretos(alpha, num):\n", " a = np.random.pareto(alpha, size=(1000, num))\n", " sample = a.sum(axis=1)\n", " return sample" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And here's a function that plots the results." ] }, { "cell_type": "code", "execution_count": 88, "metadata": {}, "outputs": [], "source": [ "def plot_paretos(mean, nums):\n", " for num in nums:\n", " sample = sum_of_paretos(mean, num)\n", "\n", " plot_normal_model(sample, color='gray')\n", " Cdf.from_seq(sample).plot(label=f'num = {num}')\n", "\n", " plt.xlabel('Total')\n", " plt.ylabel('CDF')\n", " plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "With `alpha=3` the Pareto distribution is relatively well-behaved, and the sum converges to a normal distribution with a moderate number of values." ] }, { "cell_type": "code", "execution_count": 89, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "alpha = 3\n", "plot_paretos(alpha, [10, 20, 50])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "With `alpha=2`, we don't get very good convergence even with 1000 values." ] }, { "cell_type": "code", "execution_count": 90, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "alpha = 2\n", "plot_paretos(alpha, [200, 500, 1000])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "With `alpha=1.5`, it's even worse." ] }, { "cell_type": "code", "execution_count": 53, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "alpha = 1.5\n", "plot_paretos(alpha, [2000, 5000, 10000])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And with `alpha=1`, it's beyond hopeless." ] }, { "cell_type": "code", "execution_count": 91, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "alpha = 1\n", "plot_paretos(alpha, [10000, 20000, 50000])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In fact, when `alpha` is 2 or less, the variance of the Pareto distribution is infinite, and the central limit theorem does not apply. The disrtribution of the sum never converges to a normal distribution.\n", "\n", "However, there is no practical difference between a distribution like Pareto that never converges and other high-variance distributions that converge in theory, but only with an impractical number of values." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Summary\n", "\n", "The central limit theorem is an important result in mathematical statistics. And it explains why so many distributions in the natural and engineered world are approximately normal.\n", "\n", "But it doesn't always apply:\n", "\n", "* In theory the central limit theorem doesn't apply when variance is infinite.\n", "\n", "* In practice it might be irrelevant when variance is high.\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "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": "3.7.6" } }, "nbformat": 4, "nbformat_minor": 2 }