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Breaking the central limit theorem with the Cauchy distribution
{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"ExecuteTime": {
"end_time": "2017-10-20T16:26:14.389993Z",
"start_time": "2017-10-20T16:26:13.674284Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Populating the interactive namespace from numpy and matplotlib\n"
]
}
],
"source": [
"%pylab inline"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"ExecuteTime": {
"end_time": "2017-10-20T16:26:15.661999Z",
"start_time": "2017-10-20T16:26:14.393524Z"
}
},
"outputs": [],
"source": [
"from scipy.stats import cauchy, poisson, normaltest\n",
"import seaborn\n",
"seaborn.set_style(\"whitegrid\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Central Limit Theorem\n",
"\n",
"The central limit theorem roughly states that for most distributions, if we perform many independent draws from that distribution, the mean of those draws will tend to normality as the number of draws increases. Critically, this applies to *most* non-normal distributions.\n",
"\n",
"Does it apply everywhere? No. An assumption of the CLT is that the target distribution has finite variance. The [Cauchy](https://en.wikipedia.org/wiki/Cauchy_distribution) distribution which has *infinite* variance breaks this assumption and so CLT does not apply. Let's see how this looks:"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"ExecuteTime": {
"end_time": "2017-10-20T16:26:19.218244Z",
"start_time": "2017-10-20T16:26:15.667470Z"
}
},
"outputs": [],
"source": [
"n_samples = 1000\n",
"n_means = 10000\n",
"\n",
"cauchy_means = array(\n",
" [mean(cauchy.rvs(size=n_samples)) for _ in range(n_means)])\n",
"\n",
"poisson_means = array(\n",
" [mean(poisson.rvs(size=n_samples, mu=.9)) for _ in range(n_means)])"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"ExecuteTime": {
"end_time": "2017-10-20T16:26:19.233479Z",
"start_time": "2017-10-20T16:26:19.221394Z"
}
},
"outputs": [],
"source": [
"def plot_kde_samples(samples, n, label, ax):\n",
" seaborn.kdeplot(samples[:n], ax=ax)\n",
" n_score = normaltest(samples[:n])\n",
" ax.set_title(f\"{label} at $n={n}$, $p={n_score[1]:.3f}$\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Plot results\n",
"\n",
"Here, I'll plot the results for different size estimates of the means for each distribution. The [normality test](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.normaltest.html) is based on D’Agostino and Pearson’s, so the null assumption is that the distribution is normal, and we can reject that assumption with a sufficiently low $p$ value."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"ExecuteTime": {
"end_time": "2017-10-20T16:26:21.198550Z",
"start_time": "2017-10-20T16:26:19.237033Z"
}
},
"outputs": [
{
"data": {
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OHcKOHTvA5XLRtGlTfPfddwCAoqIizJkzBwkJCRCLxVi5ciWOHTsGoVCIuXPnAgBOnDiB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\nC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zekuK2T7oPPE6nibSz21qYlps3jRuaX21mwNedhlK9Tm5zfycoUQ7wdcSo2m/ZHGhEv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\ntR3DDPwOAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x112774b38>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, axes = subplots(nrows=3, ncols=2, figsize=(8,8))\n",
"axes = axes.flat\n",
"\n",
"plot_kde_samples(cauchy_means, 20, \"Cauchy\", axes[1])\n",
"plot_kde_samples(cauchy_means, 1000, \"Cauchy\", axes[3])\n",
"plot_kde_samples(cauchy_means, 10000, \"Cauchy\", axes[5])\n",
"\n",
"plot_kde_samples(poisson_means, 20, \"Poisson\", axes[0])\n",
"plot_kde_samples(poisson_means, 1000, \"Poisson\", axes[2])\n",
"plot_kde_samples(poisson_means, 10000, \"Poisson\", axes[4])\n",
"\n",
"fig.suptitle(\"CLT for Cauchy and Poisson\");"
]
},
{
"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": "3.6.1"
},
"varInspector": {
"cols": {
"lenName": 16,
"lenType": 16,
"lenVar": 40
},
"kernels_config": {
"python": {
"delete_cmd_postfix": "",
"delete_cmd_prefix": "del ",
"library": "var_list.py",
"varRefreshCmd": "print(var_dic_list())"
},
"r": {
"delete_cmd_postfix": ") ",
"delete_cmd_prefix": "rm(",
"library": "var_list.r",
"varRefreshCmd": "cat(var_dic_list()) "
}
},
"position": {
"height": "283px",
"left": "590px",
"right": "20px",
"top": "120px",
"width": "360px"
},
"types_to_exclude": [
"module",
"function",
"builtin_function_or_method",
"instance",
"_Feature"
],
"window_display": false
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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