{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# What Are Fat Tails? #\n",
    "\n",
    "Here we discuss some of the theoretical underpinnings of fat-tail distributions, informed mainly by Nassim Taleb in [SCOFT](references.ipynb).\n",
    "\n",
    "## Thin vs. Fat ##\n",
    "\n",
    "Probabliity distributions range from thin-tailed to fat-tailed. Taleb formally defines a fat-tailed distribution as a distribution where the tail events dominate its characteristics and impacts. Others refer to this root class as \"heavy\" tails, reserving \"fat\" tails for the most dramatic subset.\n",
    "\n",
    "Taleb suggests \"subexponential\" distributions as the borderline between thin and fat tails, which are defined in terms of the slope of their survival functions in the tails:\n",
    "    + the slope of thin-tailed survivial functions (such as the Guassian) decay exponentially towards $\\infty$, usually towards some upper bound evident on a log-log plot.\n",
    "    + the slope of heavy-tailed survival functions decay at a rate slower than exponential, at a minimum, with the more dramatic fat tails decaying linearily (or not decaying at all).\n",
    "    + Subexponential distributions will have a kurtosis > 3 (kurtosis of Gaussian)\n",
    "\n",
    "## The Borderline Sigmoid ##\n",
    "\n",
    "Taleb defines the borderline distribution between thin and fat where the ratio of the power over the root is 1 for a two-tailed distribution:\n",
    "\n",
    "$$\\lim\\limits_{x\\to+\\infty}\\frac{F(x)^n}{F(nx)} = 1$$\n",
    "\n",
    "A sample of such a distribution is suggested as:\n",
    "\n",
    "$$\n",
    "F(x) = \\frac{1}{2}(1 - tanh(kx)), k > 0\n",
    "\\\\ f(x) = \\frac{1}{2}ksech^2(kx)\n",
    "$$\n",
    "\n",
    "The kurtosis of the above distribution is 4.2, which is greater than 3 (the kurtosis of the standard Gaussian), and so it has slightly fatter tails.\n",
    "\n",
    "\n",
    "This distribution is available in the package as `BLineSigmoid`. In the figure below, we can see the slightest difference in the head, shoulders, and tail versus the Gaussian."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "nbsphinx": "hidden"
   },
   "outputs": [],
   "source": [
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "\n",
    "import seaborn as sns; sns.set(style = 'whitegrid')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import scipy.stats as scist\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "import phat as ph\n",
    "\n",
    "k = 1\n",
    "x = np.linspace(0,4,100)\n",
    "bline = ph.dists.BLineSig(k)\n",
    "norm = scist.norm(scale=bline.var())\n",
    "\n",
    "fig, ax = plt.subplots(1,1,figsize=(10,6))\n",
    "ax.plot(x, bline.pdf(x), label='Borderline Sigmoid')\n",
    "ax.plot(x, norm.pdf(x) , label='Gaussian')\n",
    "\n",
    "ax.set_ylabel('P(X=x)', loc='top', rotation='horizontal')\n",
    "ax.set_xlabel('Log x', loc='right')\n",
    "\n",
    "plt.legend()\n",
    "\n",
    "ax.grid(False)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Devil is in the Tails ##\n",
    "\n",
    "So a distribution need only have kurtosis > 3 to be classified as fat-tailed (at least by Taleb). But we can further distinguish between fat tails by the change in slope of the tail as $n\\to\\infty$. This slope is referred to as the \"tail index\", designated $\\alpha$ by Taleb (and many other greeks by various others).\n",
    "\n",
    "Thin tails such as the Gaussian have non-linear tails whose slopes decay towards infinity, i.e. $\\alpha\\to\\infty$ as $n\\to\\infty$, meaning the distributions reach an effective maximum. At this level, E(X | X > x) = X, meaning there are no values $> x$ expected in the distribution.\n",
    "\n",
    "The more dramatic fat tails tend to a non-zero, non-infinite slope, *meaning they have no effective maximum*. These include the Power Laws. The Power Laws also result in other strange characteristics such as undefined moments including undefined variance ($\\alpha < 2$) *and* undefined mean ($\\alpha < 1$).\n",
    "\n",
    "Below we show log-log scales of the Gaussian thin tail versus two subexponential distributions (each with tail index $\\alpha = 3$).\n",
    "\n",
    "+ the Lognormal, which is a fat tail masquerading as a power law and is revealed as an imposter at larger $x$.\n",
    "+ the Student's T, which is often used as a power law, though it only tends to one at larger $x$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "tags": [
     "hide_input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x432 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import warnings\n",
    "\n",
    "k, df = 3, 3\n",
    "lognorm = scist.lognorm(s=k)\n",
    "t = scist.t(df=df)\n",
    "\n",
    "x = np.logspace(.15, 50,10000, dtype=np.float64)\n",
    "\n",
    "fig, (ax1,ax2) = plt.subplots(1,2,figsize=(20,6))\n",
    "\n",
    "with np.errstate(divide='ignore'):\n",
    "    with warnings.catch_warnings():\n",
    "        warnings.simplefilter(\"ignore\")\n",
    "        ax1.plot(np.log(x), -np.log(scist.norm.pdf(x, scale=1)), label='Gaussian')\n",
    "        ax1.plot(np.log(x), -np.log(lognorm.pdf(x)), label='Lognormal (3)')\n",
    "        ax1.plot(np.log(x), -np.log(t.pdf(x)), label='T (3)')\n",
    "\n",
    "ax1.set_xscale('log')\n",
    "ax1.set_yscale('log')\n",
    "\n",
    "ax1.set_xlim((0.1, 400))\n",
    "ylim = ax1.get_ylim()\n",
    "ax1.set_ylim(ylim[::-1])\n",
    "\n",
    "yticks = ax1.get_yticks()\n",
    "ax1.set_yticks(yticks[2:-2])\n",
    "ax1.set_yticklabels(1/yticks[2:-2])\n",
    "\n",
    "ax1.set_ylabel('Log P(x)', loc='top', rotation='horizontal')\n",
    "ax1.set_xlabel('Log x', loc='right')\n",
    "\n",
    "ax1.legend()\n",
    "ax1.set_title('Probability Density Function')\n",
    "\n",
    "with np.errstate(divide='ignore'):\n",
    "    with warnings.catch_warnings():\n",
    "        warnings.simplefilter(\"ignore\")\n",
    "        ax2.plot(x, scist.norm.sf(x, scale=1), label='Gaussian')\n",
    "        ax2.plot(x, lognorm.sf(x), label='Lognormal (3)')\n",
    "        ax2.plot(x, t.sf(x), label='T (3)')\n",
    "\n",
    "ax2.set_xscale('log')\n",
    "ax2.set_yscale('log')\n",
    "\n",
    "ax2.set_ylabel('Log P(X>x)', loc='top', rotation='horizontal')\n",
    "ax2.set_xlabel('Log x', loc='right')\n",
    "\n",
    "ax2.set_title('Survival Function')\n",
    "ax2.legend()\n",
    "\n",
    "ax1.grid(False)\n",
    "ax2.grid(False)\n",
    "\n",
    "plt.suptitle('In The Tails', y=1.01, size='x-large')\n",
    "fig.subplots_adjust(wspace=.3)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, above, we see the PDF of the three distributions with the Gaussian evidencing exponential decay almost immediately, the lognormal decaying into the tails, and the T distribution becoming linear further into the tails. The Survival Function accentuates the difference."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Scale Invariance ##\n",
    "\n",
    "The property of a linear slope in the tails of a distribution is known as \"scale invariance\" (again see [SCOFT](#References)). It means that for a scalar increase in $x$, the probability of occurence decays at a constant rate. Thin-tailed and non-power law fat tails are \"scale variant\", meaning that the probability of occurence decays at an increasing rate.\n",
    "\n",
    "This is a remarkably powerful effect, as outcomes far out in the tails of power laws are orders of magnitude *of orders of magnitude* (not a typo) more likely. This is not to say that tail events will occur more often; instead it means that *when tail events do occur, they will be much larger*.\n",
    "\n",
    "This impact is most readily seen when we decrease the tail index, thereby decreasing the rate of (linear) decay of the survival function, and watch the impact on the first and second moments."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>$\\mu$</th>\n",
       "      <th>$\\sigma^2$</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$\\alpha$</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.5</td>\n",
       "      <td>0.75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2.0</td>\n",
       "      <td>inf</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>inf</td>\n",
       "      <td>inf</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          $\\mu$  $\\sigma^2$\n",
       "$\\alpha$                   \n",
       "3           1.5        0.75\n",
       "2           2.0         inf\n",
       "1           inf         inf"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "alphas = pd.Index([3,2,1], name=r'$\\alpha$')\n",
    "chars = [(scist.pareto(alpha).mean(), scist.pareto(alpha).var()) for alpha in alphas]\n",
    "df = pd.DataFrame(chars, columns=[r'$\\mu$', r'$\\sigma^2$'], index=alphas)\n",
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With a tail index of 2, the potential for extreme values makes the variance undefined. With a tail index of 1 extreme values can be so large that the distribution has no mean."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Scale invariance is mathematically defined as:\n",
    "\n",
    "$$\n",
    "P(X>x) = L(x)x^{-a}\n",
    "$$\n",
    "\n",
    "where $L(x)$ is a slow-varying function defined as:\n",
    "\n",
    "$$\n",
    "\\lim\\limits_{x\\to\\infty} \\frac{L(cx)}{L(x)} = 1\n",
    "$$\n",
    "\n",
    "$L(x)$ can simply be replaced with a constant, as per the Pareto distribution:\n",
    "\n",
    "$$\n",
    "P(X>x) = x_{min}x^{-a}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see this property of scale invariance most clearly in the table below, where we compare the Gaussian, Lognormal, T, Pareto, and the LogPareto scale ratios at increaseing $k$. This is an expanded version of the table found [SCOFT](references.ipynb)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       "</style>\n",
       "<table id=\"T_f13fc_\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank\" >&nbsp;</th>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th class=\"col_heading level0 col0\" colspan=\"2\">Gaussian</th>\n",
       "      <th class=\"col_heading level0 col2\" colspan=\"2\">Lognorm (2)</th>\n",
       "      <th class=\"col_heading level0 col4\" colspan=\"2\">T (2)</th>\n",
       "      <th class=\"col_heading level0 col6\" colspan=\"2\">Pareto (2)</th>\n",
       "      <th class=\"col_heading level0 col8\" colspan=\"2\">Logpareto (2)</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th class=\"blank\" >&nbsp;</th>\n",
       "      <th class=\"blank level1\" >&nbsp;</th>\n",
       "      <th class=\"col_heading level1 col0\" >$P(X > k)^{-1}$</th>\n",
       "      <th class=\"col_heading level1 col1\" >$\\frac{P(X > k)}{P(X > nk)}$</th>\n",
       "      <th class=\"col_heading level1 col2\" >$P(X > k)^{-1}$</th>\n",
       "      <th class=\"col_heading level1 col3\" >$\\frac{P(X > k)}{P(X > nk)}$</th>\n",
       "      <th class=\"col_heading level1 col4\" >$P(X > k)^{-1}$</th>\n",
       "      <th class=\"col_heading level1 col5\" >$\\frac{P(X > k)}{P(X > nk)}$</th>\n",
       "      <th class=\"col_heading level1 col6\" >$P(X > k)^{-1}$</th>\n",
       "      <th class=\"col_heading level1 col7\" >$\\frac{P(X > k)}{P(X > nk)}$</th>\n",
       "      <th class=\"col_heading level1 col8\" >$P(X > k)^{-1}$</th>\n",
       "      <th class=\"col_heading level1 col9\" >$\\frac{P(X > k)}{P(X > nk)}$</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th class=\"index_name level0\" >n</th>\n",
       "      <th class=\"index_name level1\" >k</th>\n",
       "      <th class=\"blank col0\" >&nbsp;</th>\n",
       "      <th class=\"blank col1\" >&nbsp;</th>\n",
       "      <th class=\"blank col2\" >&nbsp;</th>\n",
       "      <th class=\"blank col3\" >&nbsp;</th>\n",
       "      <th class=\"blank col4\" >&nbsp;</th>\n",
       "      <th class=\"blank col5\" >&nbsp;</th>\n",
       "      <th class=\"blank col6\" >&nbsp;</th>\n",
       "      <th class=\"blank col7\" >&nbsp;</th>\n",
       "      <th class=\"blank col8\" >&nbsp;</th>\n",
       "      <th class=\"blank col9\" >&nbsp;</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_f13fc_level0_row0\" class=\"row_heading level0 row0\" rowspan=\"7\">1</th>\n",
       "      <th id=\"T_f13fc_level1_row0\" class=\"row_heading level1 row0\" >2</th>\n",
       "      <td id=\"T_f13fc_row0_col0\" class=\"data row0 col0\" >4E+01</td>\n",
       "      <td id=\"T_f13fc_row0_col1\" class=\"data row0 col1\" >1E+00</td>\n",
       "      <td id=\"T_f13fc_row0_col2\" class=\"data row0 col2\" >2.743817</td>\n",
       "      <td id=\"T_f13fc_row0_col3\" class=\"data row0 col3\" >1.000000</td>\n",
       "      <td id=\"T_f13fc_row0_col4\" class=\"data row0 col4\" >11</td>\n",
       "      <td id=\"T_f13fc_row0_col5\" class=\"data row0 col5\" >1.0</td>\n",
       "      <td id=\"T_f13fc_row0_col6\" class=\"data row0 col6\" >4</td>\n",
       "      <td id=\"T_f13fc_row0_col7\" class=\"data row0 col7\" >1</td>\n",
       "      <td id=\"T_f13fc_row0_col8\" class=\"data row0 col8\" >0.5</td>\n",
       "      <td id=\"T_f13fc_row0_col9\" class=\"data row0 col9\" >1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_f13fc_level1_row1\" class=\"row_heading level1 row1\" >4</th>\n",
       "      <td id=\"T_f13fc_row1_col0\" class=\"data row1 col0\" >3E+04</td>\n",
       "      <td id=\"T_f13fc_row1_col1\" class=\"data row1 col1\" >1E+00</td>\n",
       "      <td id=\"T_f13fc_row1_col2\" class=\"data row1 col2\" >4.096537</td>\n",
       "      <td id=\"T_f13fc_row1_col3\" class=\"data row1 col3\" >1.000000</td>\n",
       "      <td id=\"T_f13fc_row1_col4\" class=\"data row1 col4\" >35</td>\n",
       "      <td id=\"T_f13fc_row1_col5\" class=\"data row1 col5\" >1.0</td>\n",
       "      <td id=\"T_f13fc_row1_col6\" class=\"data row1 col6\" >16</td>\n",
       "      <td id=\"T_f13fc_row1_col7\" class=\"data row1 col7\" >1</td>\n",
       "      <td id=\"T_f13fc_row1_col8\" class=\"data row1 col8\" >1.9</td>\n",
       "      <td id=\"T_f13fc_row1_col9\" class=\"data row1 col9\" >1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_f13fc_level1_row2\" class=\"row_heading level1 row2\" >6</th>\n",
       "      <td id=\"T_f13fc_row2_col0\" class=\"data row2 col0\" >1E+09</td>\n",
       "      <td id=\"T_f13fc_row2_col1\" class=\"data row2 col1\" >1E+00</td>\n",
       "      <td id=\"T_f13fc_row2_col2\" class=\"data row2 col2\" >5.400778</td>\n",
       "      <td id=\"T_f13fc_row2_col3\" class=\"data row2 col3\" >1.000000</td>\n",
       "      <td id=\"T_f13fc_row2_col4\" class=\"data row2 col4\" >75</td>\n",
       "      <td id=\"T_f13fc_row2_col5\" class=\"data row2 col5\" >1.0</td>\n",
       "      <td id=\"T_f13fc_row2_col6\" class=\"data row2 col6\" >36</td>\n",
       "      <td id=\"T_f13fc_row2_col7\" class=\"data row2 col7\" >1</td>\n",
       "      <td id=\"T_f13fc_row2_col8\" class=\"data row2 col8\" >3.2</td>\n",
       "      <td id=\"T_f13fc_row2_col9\" class=\"data row2 col9\" >1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_f13fc_level1_row3\" class=\"row_heading level1 row3\" >8</th>\n",
       "      <td id=\"T_f13fc_row3_col0\" class=\"data row3 col0\" >2E+15</td>\n",
       "      <td id=\"T_f13fc_row3_col1\" class=\"data row3 col1\" >1E+00</td>\n",
       "      <td id=\"T_f13fc_row3_col2\" class=\"data row3 col2\" >6.700849</td>\n",
       "      <td id=\"T_f13fc_row3_col3\" class=\"data row3 col3\" >1.000000</td>\n",
       "      <td id=\"T_f13fc_row3_col4\" class=\"data row3 col4\" >131</td>\n",
       "      <td id=\"T_f13fc_row3_col5\" class=\"data row3 col5\" >1.0</td>\n",
       "      <td id=\"T_f13fc_row3_col6\" class=\"data row3 col6\" >64</td>\n",
       "      <td id=\"T_f13fc_row3_col7\" class=\"data row3 col7\" >1</td>\n",
       "      <td id=\"T_f13fc_row3_col8\" class=\"data row3 col8\" >4.3</td>\n",
       "      <td id=\"T_f13fc_row3_col9\" class=\"data row3 col9\" >1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_f13fc_level1_row4\" class=\"row_heading level1 row4\" >10</th>\n",
       "      <td id=\"T_f13fc_row4_col0\" class=\"data row4 col0\" >1E+23</td>\n",
       "      <td id=\"T_f13fc_row4_col1\" class=\"data row4 col1\" >1E+00</td>\n",
       "      <td id=\"T_f13fc_row4_col2\" class=\"data row4 col2\" >8.012438</td>\n",
       "      <td id=\"T_f13fc_row4_col3\" class=\"data row4 col3\" >1.000000</td>\n",
       "      <td id=\"T_f13fc_row4_col4\" class=\"data row4 col4\" >203</td>\n",
       "      <td id=\"T_f13fc_row4_col5\" class=\"data row4 col5\" >1.0</td>\n",
       "      <td id=\"T_f13fc_row4_col6\" class=\"data row4 col6\" >100</td>\n",
       "      <td id=\"T_f13fc_row4_col7\" class=\"data row4 col7\" >1</td>\n",
       "      <td id=\"T_f13fc_row4_col8\" class=\"data row4 col8\" >5.3</td>\n",
       "      <td id=\"T_f13fc_row4_col9\" class=\"data row4 col9\" >1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_f13fc_level1_row5\" class=\"row_heading level1 row5\" >12</th>\n",
       "      <td id=\"T_f13fc_row5_col0\" class=\"data row5 col0\" >6E+32</td>\n",
       "      <td id=\"T_f13fc_row5_col1\" class=\"data row5 col1\" >1E+00</td>\n",
       "      <td id=\"T_f13fc_row5_col2\" class=\"data row5 col2\" >9.342767</td>\n",
       "      <td id=\"T_f13fc_row5_col3\" class=\"data row5 col3\" >1.000000</td>\n",
       "      <td id=\"T_f13fc_row5_col4\" class=\"data row5 col4\" >291</td>\n",
       "      <td id=\"T_f13fc_row5_col5\" class=\"data row5 col5\" >1.0</td>\n",
       "      <td id=\"T_f13fc_row5_col6\" class=\"data row5 col6\" >144</td>\n",
       "      <td id=\"T_f13fc_row5_col7\" class=\"data row5 col7\" >1</td>\n",
       "      <td id=\"T_f13fc_row5_col8\" class=\"data row5 col8\" >6.2</td>\n",
       "      <td id=\"T_f13fc_row5_col9\" class=\"data row5 col9\" >1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_f13fc_level1_row6\" class=\"row_heading level1 row6\" >14</th>\n",
       "      <td id=\"T_f13fc_row6_col0\" class=\"data row6 col0\" >1E+44</td>\n",
       "      <td id=\"T_f13fc_row6_col1\" class=\"data row6 col1\" >1E+00</td>\n",
       "      <td id=\"T_f13fc_row6_col2\" class=\"data row6 col2\" >10.695620</td>\n",
       "      <td id=\"T_f13fc_row6_col3\" class=\"data row6 col3\" >1.000000</td>\n",
       "      <td id=\"T_f13fc_row6_col4\" class=\"data row6 col4\" >395</td>\n",
       "      <td id=\"T_f13fc_row6_col5\" class=\"data row6 col5\" >1.0</td>\n",
       "      <td id=\"T_f13fc_row6_col6\" class=\"data row6 col6\" >196</td>\n",
       "      <td id=\"T_f13fc_row6_col7\" class=\"data row6 col7\" >1</td>\n",
       "      <td id=\"T_f13fc_row6_col8\" class=\"data row6 col8\" >7.0</td>\n",
       "      <td id=\"T_f13fc_row6_col9\" class=\"data row6 col9\" >1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_f13fc_level0_row7\" class=\"row_heading level0 row7\" rowspan=\"7\">2</th>\n",
       "      <th id=\"T_f13fc_level1_row7\" class=\"row_heading level1 row7\" >2</th>\n",
       "      <td id=\"T_f13fc_row7_col0\" class=\"data row7 col0\" >4E+01</td>\n",
       "      <td id=\"T_f13fc_row7_col1\" class=\"data row7 col1\" >7E+02</td>\n",
       "      <td id=\"T_f13fc_row7_col2\" class=\"data row7 col2\" >2.743817</td>\n",
       "      <td id=\"T_f13fc_row7_col3\" class=\"data row7 col3\" >1.493007</td>\n",
       "      <td id=\"T_f13fc_row7_col4\" class=\"data row7 col4\" >11</td>\n",
       "      <td id=\"T_f13fc_row7_col5\" class=\"data row7 col5\" >3.2</td>\n",
       "      <td id=\"T_f13fc_row7_col6\" class=\"data row7 col6\" >4</td>\n",
       "      <td id=\"T_f13fc_row7_col7\" class=\"data row7 col7\" >4</td>\n",
       "      <td id=\"T_f13fc_row7_col8\" class=\"data row7 col8\" >0.5</td>\n",
       "      <td id=\"T_f13fc_row7_col9\" class=\"data row7 col9\" >4.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_f13fc_level1_row8\" class=\"row_heading level1 row8\" >4</th>\n",
       "      <td id=\"T_f13fc_row8_col0\" class=\"data row8 col0\" >3E+04</td>\n",
       "      <td id=\"T_f13fc_row8_col1\" class=\"data row8 col1\" >5E+10</td>\n",
       "      <td id=\"T_f13fc_row8_col2\" class=\"data row8 col2\" >4.096537</td>\n",
       "      <td id=\"T_f13fc_row8_col3\" class=\"data row8 col3\" >1.635735</td>\n",
       "      <td id=\"T_f13fc_row8_col4\" class=\"data row8 col4\" >35</td>\n",
       "      <td id=\"T_f13fc_row8_col5\" class=\"data row8 col5\" >3.7</td>\n",
       "      <td id=\"T_f13fc_row8_col6\" class=\"data row8 col6\" >16</td>\n",
       "      <td id=\"T_f13fc_row8_col7\" class=\"data row8 col7\" >4</td>\n",
       "      <td id=\"T_f13fc_row8_col8\" class=\"data row8 col8\" >1.9</td>\n",
       "      <td id=\"T_f13fc_row8_col9\" class=\"data row8 col9\" >2.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_f13fc_level1_row9\" class=\"row_heading level1 row9\" >6</th>\n",
       "      <td id=\"T_f13fc_row9_col0\" class=\"data row9 col0\" >1E+09</td>\n",
       "      <td id=\"T_f13fc_row9_col1\" class=\"data row9 col1\" >6E+23</td>\n",
       "      <td id=\"T_f13fc_row9_col2\" class=\"data row9 col2\" >5.400778</td>\n",
       "      <td id=\"T_f13fc_row9_col3\" class=\"data row9 col3\" >1.729893</td>\n",
       "      <td id=\"T_f13fc_row9_col4\" class=\"data row9 col4\" >75</td>\n",
       "      <td id=\"T_f13fc_row9_col5\" class=\"data row9 col5\" >3.9</td>\n",
       "      <td id=\"T_f13fc_row9_col6\" class=\"data row9 col6\" >36</td>\n",
       "      <td id=\"T_f13fc_row9_col7\" class=\"data row9 col7\" >4</td>\n",
       "      <td id=\"T_f13fc_row9_col8\" class=\"data row9 col8\" >3.2</td>\n",
       "      <td id=\"T_f13fc_row9_col9\" class=\"data row9 col9\" >1.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_f13fc_level1_row10\" class=\"row_heading level1 row10\" >8</th>\n",
       "      <td id=\"T_f13fc_row10_col0\" class=\"data row10 col0\" >2E+15</td>\n",
       "      <td id=\"T_f13fc_row10_col1\" class=\"data row10 col1\" >1E+42</td>\n",
       "      <td id=\"T_f13fc_row10_col2\" class=\"data row10 col2\" >6.700849</td>\n",
       "      <td id=\"T_f13fc_row10_col3\" class=\"data row10 col3\" >1.801732</td>\n",
       "      <td id=\"T_f13fc_row10_col4\" class=\"data row10 col4\" >131</td>\n",
       "      <td id=\"T_f13fc_row10_col5\" class=\"data row10 col5\" >3.9</td>\n",
       "      <td id=\"T_f13fc_row10_col6\" class=\"data row10 col6\" >64</td>\n",
       "      <td id=\"T_f13fc_row10_col7\" class=\"data row10 col7\" >4</td>\n",
       "      <td id=\"T_f13fc_row10_col8\" class=\"data row10 col8\" >4.3</td>\n",
       "      <td id=\"T_f13fc_row10_col9\" class=\"data row10 col9\" >1.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_f13fc_level1_row11\" class=\"row_heading level1 row11\" >10</th>\n",
       "      <td id=\"T_f13fc_row11_col0\" class=\"data row11 col0\" >1E+23</td>\n",
       "      <td id=\"T_f13fc_row11_col1\" class=\"data row11 col1\" >3E+65</td>\n",
       "      <td id=\"T_f13fc_row11_col2\" class=\"data row11 col2\" >8.012438</td>\n",
       "      <td id=\"T_f13fc_row11_col3\" class=\"data row11 col3\" >1.860442</td>\n",
       "      <td id=\"T_f13fc_row11_col4\" class=\"data row11 col4\" >203</td>\n",
       "      <td id=\"T_f13fc_row11_col5\" class=\"data row11 col5\" >4.0</td>\n",
       "      <td id=\"T_f13fc_row11_col6\" class=\"data row11 col6\" >100</td>\n",
       "      <td id=\"T_f13fc_row11_col7\" class=\"data row11 col7\" >4</td>\n",
       "      <td id=\"T_f13fc_row11_col8\" class=\"data row11 col8\" >5.3</td>\n",
       "      <td id=\"T_f13fc_row11_col9\" class=\"data row11 col9\" >1.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_f13fc_level1_row12\" class=\"row_heading level1 row12\" >12</th>\n",
       "      <td id=\"T_f13fc_row12_col0\" class=\"data row12 col0\" >6E+32</td>\n",
       "      <td id=\"T_f13fc_row12_col1\" class=\"data row12 col1\" >1E+94</td>\n",
       "      <td id=\"T_f13fc_row12_col2\" class=\"data row12 col2\" >9.342767</td>\n",
       "      <td id=\"T_f13fc_row12_col3\" class=\"data row12 col3\" >1.910407</td>\n",
       "      <td id=\"T_f13fc_row12_col4\" class=\"data row12 col4\" >291</td>\n",
       "      <td id=\"T_f13fc_row12_col5\" class=\"data row12 col5\" >4.0</td>\n",
       "      <td id=\"T_f13fc_row12_col6\" class=\"data row12 col6\" >144</td>\n",
       "      <td id=\"T_f13fc_row12_col7\" class=\"data row12 col7\" >4</td>\n",
       "      <td id=\"T_f13fc_row12_col8\" class=\"data row12 col8\" >6.2</td>\n",
       "      <td id=\"T_f13fc_row12_col9\" class=\"data row12 col9\" >1.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_f13fc_level1_row13\" class=\"row_heading level1 row13\" >14</th>\n",
       "      <td id=\"T_f13fc_row13_col0\" class=\"data row13 col0\" >1E+44</td>\n",
       "      <td id=\"T_f13fc_row13_col1\" class=\"data row13 col1\" >1E+128</td>\n",
       "      <td id=\"T_f13fc_row13_col2\" class=\"data row13 col2\" >10.695620</td>\n",
       "      <td id=\"T_f13fc_row13_col3\" class=\"data row13 col3\" >1.954086</td>\n",
       "      <td id=\"T_f13fc_row13_col4\" class=\"data row13 col4\" >395</td>\n",
       "      <td id=\"T_f13fc_row13_col5\" class=\"data row13 col5\" >4.0</td>\n",
       "      <td id=\"T_f13fc_row13_col6\" class=\"data row13 col6\" >196</td>\n",
       "      <td id=\"T_f13fc_row13_col7\" class=\"data row13 col7\" >4</td>\n",
       "      <td id=\"T_f13fc_row13_col8\" class=\"data row13 col8\" >7.0</td>\n",
       "      <td id=\"T_f13fc_row13_col9\" class=\"data row13 col9\" >1.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_f13fc_level0_row14\" class=\"row_heading level0 row14\" rowspan=\"7\">3</th>\n",
       "      <th id=\"T_f13fc_level1_row14\" class=\"row_heading level1 row14\" >2</th>\n",
       "      <td id=\"T_f13fc_row14_col0\" class=\"data row14 col0\" >4E+01</td>\n",
       "      <td id=\"T_f13fc_row14_col1\" class=\"data row14 col1\" >2E+07</td>\n",
       "      <td id=\"T_f13fc_row14_col2\" class=\"data row14 col2\" >2.743817</td>\n",
       "      <td id=\"T_f13fc_row14_col3\" class=\"data row14 col3\" >1.968345</td>\n",
       "      <td id=\"T_f13fc_row14_col4\" class=\"data row14 col4\" >11</td>\n",
       "      <td id=\"T_f13fc_row14_col5\" class=\"data row14 col5\" >6.9</td>\n",
       "      <td id=\"T_f13fc_row14_col6\" class=\"data row14 col6\" >4</td>\n",
       "      <td id=\"T_f13fc_row14_col7\" class=\"data row14 col7\" >9</td>\n",
       "      <td id=\"T_f13fc_row14_col8\" class=\"data row14 col8\" >0.5</td>\n",
       "      <td id=\"T_f13fc_row14_col9\" class=\"data row14 col9\" >6.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_f13fc_level1_row15\" class=\"row_heading level1 row15\" >4</th>\n",
       "      <td id=\"T_f13fc_row15_col0\" class=\"data row15 col0\" >3E+04</td>\n",
       "      <td id=\"T_f13fc_row15_col1\" class=\"data row15 col1\" >2E+28</td>\n",
       "      <td id=\"T_f13fc_row15_col2\" class=\"data row15 col2\" >4.096537</td>\n",
       "      <td id=\"T_f13fc_row15_col3\" class=\"data row15 col3\" >2.280650</td>\n",
       "      <td id=\"T_f13fc_row15_col4\" class=\"data row15 col4\" >35</td>\n",
       "      <td id=\"T_f13fc_row15_col5\" class=\"data row15 col5\" >8.3</td>\n",
       "      <td id=\"T_f13fc_row15_col6\" class=\"data row15 col6\" >16</td>\n",
       "      <td id=\"T_f13fc_row15_col7\" class=\"data row15 col7\" >9</td>\n",
       "      <td id=\"T_f13fc_row15_col8\" class=\"data row15 col8\" >1.9</td>\n",
       "      <td id=\"T_f13fc_row15_col9\" class=\"data row15 col9\" >3.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_f13fc_level1_row16\" class=\"row_heading level1 row16\" >6</th>\n",
       "      <td id=\"T_f13fc_row16_col0\" class=\"data row16 col0\" >1E+09</td>\n",
       "      <td id=\"T_f13fc_row16_col1\" class=\"data row16 col1\" >1E+63</td>\n",
       "      <td id=\"T_f13fc_row16_col2\" class=\"data row16 col2\" >5.400778</td>\n",
       "      <td id=\"T_f13fc_row16_col3\" class=\"data row16 col3\" >2.495302</td>\n",
       "      <td id=\"T_f13fc_row16_col4\" class=\"data row16 col4\" >75</td>\n",
       "      <td id=\"T_f13fc_row16_col5\" class=\"data row16 col5\" >8.7</td>\n",
       "      <td id=\"T_f13fc_row16_col6\" class=\"data row16 col6\" >36</td>\n",
       "      <td id=\"T_f13fc_row16_col7\" class=\"data row16 col7\" >9</td>\n",
       "      <td id=\"T_f13fc_row16_col8\" class=\"data row16 col8\" >3.2</td>\n",
       "      <td id=\"T_f13fc_row16_col9\" class=\"data row16 col9\" >2.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_f13fc_level1_row17\" class=\"row_heading level1 row17\" >8</th>\n",
       "      <td id=\"T_f13fc_row17_col0\" class=\"data row17 col0\" >2E+15</td>\n",
       "      <td id=\"T_f13fc_row17_col1\" class=\"data row17 col1\" >4E+111</td>\n",
       "      <td id=\"T_f13fc_row17_col2\" class=\"data row17 col2\" >6.700849</td>\n",
       "      <td id=\"T_f13fc_row17_col3\" class=\"data row17 col3\" >2.663616</td>\n",
       "      <td id=\"T_f13fc_row17_col4\" class=\"data row17 col4\" >131</td>\n",
       "      <td id=\"T_f13fc_row17_col5\" class=\"data row17 col5\" >8.8</td>\n",
       "      <td id=\"T_f13fc_row17_col6\" class=\"data row17 col6\" >64</td>\n",
       "      <td id=\"T_f13fc_row17_col7\" class=\"data row17 col7\" >9</td>\n",
       "      <td id=\"T_f13fc_row17_col8\" class=\"data row17 col8\" >4.3</td>\n",
       "      <td id=\"T_f13fc_row17_col9\" class=\"data row17 col9\" >2.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_f13fc_level1_row18\" class=\"row_heading level1 row18\" >10</th>\n",
       "      <td id=\"T_f13fc_row18_col0\" class=\"data row18 col0\" >1E+23</td>\n",
       "      <td id=\"T_f13fc_row18_col1\" class=\"data row18 col1\" >2E+174</td>\n",
       "      <td id=\"T_f13fc_row18_col2\" class=\"data row18 col2\" >8.012438</td>\n",
       "      <td id=\"T_f13fc_row18_col3\" class=\"data row18 col3\" >2.804049</td>\n",
       "      <td id=\"T_f13fc_row18_col4\" class=\"data row18 col4\" >203</td>\n",
       "      <td id=\"T_f13fc_row18_col5\" class=\"data row18 col5\" >8.9</td>\n",
       "      <td id=\"T_f13fc_row18_col6\" class=\"data row18 col6\" >100</td>\n",
       "      <td id=\"T_f13fc_row18_col7\" class=\"data row18 col7\" >9</td>\n",
       "      <td id=\"T_f13fc_row18_col8\" class=\"data row18 col8\" >5.3</td>\n",
       "      <td id=\"T_f13fc_row18_col9\" class=\"data row18 col9\" >2.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_f13fc_level1_row19\" class=\"row_heading level1 row19\" >12</th>\n",
       "      <td id=\"T_f13fc_row19_col0\" class=\"data row19 col0\" >6E+32</td>\n",
       "      <td id=\"T_f13fc_row19_col1\" class=\"data row19 col1\" >4E+250</td>\n",
       "      <td id=\"T_f13fc_row19_col2\" class=\"data row19 col2\" >9.342767</td>\n",
       "      <td id=\"T_f13fc_row19_col3\" class=\"data row19 col3\" >2.925584</td>\n",
       "      <td id=\"T_f13fc_row19_col4\" class=\"data row19 col4\" >291</td>\n",
       "      <td id=\"T_f13fc_row19_col5\" class=\"data row19 col5\" >8.9</td>\n",
       "      <td id=\"T_f13fc_row19_col6\" class=\"data row19 col6\" >144</td>\n",
       "      <td id=\"T_f13fc_row19_col7\" class=\"data row19 col7\" >9</td>\n",
       "      <td id=\"T_f13fc_row19_col8\" class=\"data row19 col8\" >6.2</td>\n",
       "      <td id=\"T_f13fc_row19_col9\" class=\"data row19 col9\" >2.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_f13fc_level1_row20\" class=\"row_heading level1 row20\" >14</th>\n",
       "      <td id=\"T_f13fc_row20_col0\" class=\"data row20 col0\" >1E+44</td>\n",
       "      <td id=\"T_f13fc_row20_col1\" class=\"data row20 col1\" >INF</td>\n",
       "      <td id=\"T_f13fc_row20_col2\" class=\"data row20 col2\" >10.695620</td>\n",
       "      <td id=\"T_f13fc_row20_col3\" class=\"data row20 col3\" >3.033336</td>\n",
       "      <td id=\"T_f13fc_row20_col4\" class=\"data row20 col4\" >395</td>\n",
       "      <td id=\"T_f13fc_row20_col5\" class=\"data row20 col5\" >8.9</td>\n",
       "      <td id=\"T_f13fc_row20_col6\" class=\"data row20 col6\" >196</td>\n",
       "      <td id=\"T_f13fc_row20_col7\" class=\"data row20 col7\" >9</td>\n",
       "      <td id=\"T_f13fc_row20_col8\" class=\"data row20 col8\" >7.0</td>\n",
       "      <td id=\"T_f13fc_row20_col9\" class=\"data row20 col9\" >2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_f13fc_level0_row21\" class=\"row_heading level0 row21\" rowspan=\"7\">4</th>\n",
       "      <th id=\"T_f13fc_level1_row21\" class=\"row_heading level1 row21\" >2</th>\n",
       "      <td id=\"T_f13fc_row21_col0\" class=\"data row21 col0\" >4E+01</td>\n",
       "      <td id=\"T_f13fc_row21_col1\" class=\"data row21 col1\" >4E+13</td>\n",
       "      <td id=\"T_f13fc_row21_col2\" class=\"data row21 col2\" >2.743817</td>\n",
       "      <td id=\"T_f13fc_row21_col3\" class=\"data row21 col3\" >2.442164</td>\n",
       "      <td id=\"T_f13fc_row21_col4\" class=\"data row21 col4\" >11</td>\n",
       "      <td id=\"T_f13fc_row21_col5\" class=\"data row21 col5\" >12.0</td>\n",
       "      <td id=\"T_f13fc_row21_col6\" class=\"data row21 col6\" >4</td>\n",
       "      <td id=\"T_f13fc_row21_col7\" class=\"data row21 col7\" >16</td>\n",
       "      <td id=\"T_f13fc_row21_col8\" class=\"data row21 col8\" >0.5</td>\n",
       "      <td id=\"T_f13fc_row21_col9\" class=\"data row21 col9\" >9.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_f13fc_level1_row22\" class=\"row_heading level1 row22\" >4</th>\n",
       "      <td id=\"T_f13fc_row22_col0\" class=\"data row22 col0\" >3E+04</td>\n",
       "      <td id=\"T_f13fc_row22_col1\" class=\"data row22 col1\" >5E+52</td>\n",
       "      <td id=\"T_f13fc_row22_col2\" class=\"data row22 col2\" >4.096537</td>\n",
       "      <td id=\"T_f13fc_row22_col3\" class=\"data row22 col3\" >2.947156</td>\n",
       "      <td id=\"T_f13fc_row22_col4\" class=\"data row22 col4\" >35</td>\n",
       "      <td id=\"T_f13fc_row22_col5\" class=\"data row22 col5\" >14.7</td>\n",
       "      <td id=\"T_f13fc_row22_col6\" class=\"data row22 col6\" >16</td>\n",
       "      <td id=\"T_f13fc_row22_col7\" class=\"data row22 col7\" >16</td>\n",
       "      <td id=\"T_f13fc_row22_col8\" class=\"data row22 col8\" >1.9</td>\n",
       "      <td id=\"T_f13fc_row22_col9\" class=\"data row22 col9\" >4.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_f13fc_level1_row23\" class=\"row_heading level1 row23\" >6</th>\n",
       "      <td id=\"T_f13fc_row23_col0\" class=\"data row23 col0\" >1E+09</td>\n",
       "      <td id=\"T_f13fc_row23_col1\" class=\"data row23 col1\" >7E+117</td>\n",
       "      <td id=\"T_f13fc_row23_col2\" class=\"data row23 col2\" >5.400778</td>\n",
       "      <td id=\"T_f13fc_row23_col3\" class=\"data row23 col3\" >3.304799</td>\n",
       "      <td id=\"T_f13fc_row23_col4\" class=\"data row23 col4\" >75</td>\n",
       "      <td id=\"T_f13fc_row23_col5\" class=\"data row23 col5\" >15.4</td>\n",
       "      <td id=\"T_f13fc_row23_col6\" class=\"data row23 col6\" >36</td>\n",
       "      <td id=\"T_f13fc_row23_col7\" class=\"data row23 col7\" >16</td>\n",
       "      <td id=\"T_f13fc_row23_col8\" class=\"data row23 col8\" >3.2</td>\n",
       "      <td id=\"T_f13fc_row23_col9\" class=\"data row23 col9\" >3.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_f13fc_level1_row24\" class=\"row_heading level1 row24\" >8</th>\n",
       "      <td id=\"T_f13fc_row24_col0\" class=\"data row24 col0\" >2E+15</td>\n",
       "      <td id=\"T_f13fc_row24_col1\" class=\"data row24 col1\" >1E+209</td>\n",
       "      <td id=\"T_f13fc_row24_col2\" class=\"data row24 col2\" >6.700849</td>\n",
       "      <td id=\"T_f13fc_row24_col3\" class=\"data row24 col3\" >3.590865</td>\n",
       "      <td id=\"T_f13fc_row24_col4\" class=\"data row24 col4\" >131</td>\n",
       "      <td id=\"T_f13fc_row24_col5\" class=\"data row24 col5\" >15.7</td>\n",
       "      <td id=\"T_f13fc_row24_col6\" class=\"data row24 col6\" >64</td>\n",
       "      <td id=\"T_f13fc_row24_col7\" class=\"data row24 col7\" >16</td>\n",
       "      <td id=\"T_f13fc_row24_col8\" class=\"data row24 col8\" >4.3</td>\n",
       "      <td id=\"T_f13fc_row24_col9\" class=\"data row24 col9\" >2.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_f13fc_level1_row25\" class=\"row_heading level1 row25\" >10</th>\n",
       "      <td id=\"T_f13fc_row25_col0\" class=\"data row25 col0\" >1E+23</td>\n",
       "      <td id=\"T_f13fc_row25_col1\" class=\"data row25 col1\" >INF</td>\n",
       "      <td id=\"T_f13fc_row25_col2\" class=\"data row25 col2\" >8.012438</td>\n",
       "      <td id=\"T_f13fc_row25_col3\" class=\"data row25 col3\" >3.833161</td>\n",
       "      <td id=\"T_f13fc_row25_col4\" class=\"data row25 col4\" >203</td>\n",
       "      <td id=\"T_f13fc_row25_col5\" class=\"data row25 col5\" >15.8</td>\n",
       "      <td id=\"T_f13fc_row25_col6\" class=\"data row25 col6\" >100</td>\n",
       "      <td id=\"T_f13fc_row25_col7\" class=\"data row25 col7\" >16</td>\n",
       "      <td id=\"T_f13fc_row25_col8\" class=\"data row25 col8\" >5.3</td>\n",
       "      <td id=\"T_f13fc_row25_col9\" class=\"data row25 col9\" >2.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_f13fc_level1_row26\" class=\"row_heading level1 row26\" >12</th>\n",
       "      <td id=\"T_f13fc_row26_col0\" class=\"data row26 col0\" >6E+32</td>\n",
       "      <td id=\"T_f13fc_row26_col1\" class=\"data row26 col1\" >INF</td>\n",
       "      <td id=\"T_f13fc_row26_col2\" class=\"data row26 col2\" >9.342767</td>\n",
       "      <td id=\"T_f13fc_row26_col3\" class=\"data row26 col3\" >4.045406</td>\n",
       "      <td id=\"T_f13fc_row26_col4\" class=\"data row26 col4\" >291</td>\n",
       "      <td id=\"T_f13fc_row26_col5\" class=\"data row26 col5\" >15.8</td>\n",
       "      <td id=\"T_f13fc_row26_col6\" class=\"data row26 col6\" >144</td>\n",
       "      <td id=\"T_f13fc_row26_col7\" class=\"data row26 col7\" >16</td>\n",
       "      <td id=\"T_f13fc_row26_col8\" class=\"data row26 col8\" >6.2</td>\n",
       "      <td id=\"T_f13fc_row26_col9\" class=\"data row26 col9\" >2.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_f13fc_level1_row27\" class=\"row_heading level1 row27\" >14</th>\n",
       "      <td id=\"T_f13fc_row27_col0\" class=\"data row27 col0\" >1E+44</td>\n",
       "      <td id=\"T_f13fc_row27_col1\" class=\"data row27 col1\" >INF</td>\n",
       "      <td id=\"T_f13fc_row27_col2\" class=\"data row27 col2\" >10.695620</td>\n",
       "      <td id=\"T_f13fc_row27_col3\" class=\"data row27 col3\" >4.235510</td>\n",
       "      <td id=\"T_f13fc_row27_col4\" class=\"data row27 col4\" >395</td>\n",
       "      <td id=\"T_f13fc_row27_col5\" class=\"data row27 col5\" >15.9</td>\n",
       "      <td id=\"T_f13fc_row27_col6\" class=\"data row27 col6\" >196</td>\n",
       "      <td id=\"T_f13fc_row27_col7\" class=\"data row27 col7\" >16</td>\n",
       "      <td id=\"T_f13fc_row27_col8\" class=\"data row27 col8\" >7.0</td>\n",
       "      <td id=\"T_f13fc_row27_col9\" class=\"data row27 col9\" >2.3</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x199068d30>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "\n",
    "def tail_scale(p, dist):\n",
    "    return dist.sf(p[1]) / dist.sf(p[0]*p[1])\n",
    "\n",
    "norm = scist.norm()\n",
    "lg = scist.lognorm(2)\n",
    "t = scist.t(2)\n",
    "pareto = scist.pareto(2)\n",
    "lp = ph.dists.LogPareto(2)\n",
    "dists = [norm, lg, t, pareto, lp]\n",
    "\n",
    "n = [i for i in range(1,5)]\n",
    "k = [i for i in range(2,16,2)]\n",
    "\n",
    "index = pd.MultiIndex.from_product([n, k], names=['n', 'k'])\n",
    "\n",
    "l1 = ['Gaussian', 'Lognorm (2)', \"T (2)\", 'Pareto (2)', 'Logpareto (2)']\n",
    "l2 = [r'$P(X > k)^{-1}$', r'$\\frac{P(X > k)}{P(X > nk)}$']\n",
    "cols = pd.MultiIndex.from_product((l1,l2))\n",
    "\n",
    "distcomp = pd.DataFrame([], index=index, columns=cols)\n",
    "distcomp = distcomp.sort_values(['n', 'k'])\n",
    "\n",
    "with np.errstate(divide='ignore'):\n",
    "    for dist, l in zip(dists, l1):\n",
    "        distcomp.loc[:, (l, l2[0])] = [1 / dist.sf(p[1]) for p in index]\n",
    "        distcomp.loc[:, (l, l2[1])] = [tail_scale(p, dist) for p in index]\n",
    "\n",
    "cols_arr = np.array([[j for j in i] for i in distcomp.columns.to_numpy()])\n",
    "fmt1 = {tuple(col): \"{:,.0E}\" for col in distcomp.columns[:2]}\n",
    "fmt2 = {tuple(col): \"{:,.0f}\" for col in distcomp.columns[[4, 6, 7]]}\n",
    "fmt3 = {tuple(col): \"{:,.1f}\" for col in distcomp.columns[[5, 8, 9]]}\n",
    "\n",
    "distcomp.style.format({**fmt1, **fmt2, **fmt3})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Focusing on the $\\frac{P(X>k)}{P(X>nk}$ column, we can see dramatic differences between the distributions:\n",
    "\n",
    "+ Pareto: For each `n`, the value of `k` has *no impact on the ratio*. It is stable, regardless of the value of `k` used. This is the \"scale invariance\" described above.\n",
    "+ Gaussian: the complete opposite occurs, with the ratio exploding higher for minor increments of `k`.\n",
    "+ Lognormal / Student's T: the ratio for both increases much slower than the Gaussian, but still does not reach a stable value until deep into the tails. Hence, the drawback of using Student's T as a substitute for power laws and why significant literature has been devoted to use of the generalized Pareto. We can see this visually below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.logspace(.2, 2, 100000, dtype=np.float64)\n",
    "t = scist.t(3)\n",
    "pareto = scist.pareto(3)\n",
    "gp = scist.genpareto(1/3)\n",
    "convergence = np.isclose(t.sf(x), pareto.sf(x), atol=0.000001).argmax()\n",
    "\n",
    "fig, ax2 = plt.subplots(1,1,figsize=(10,6))\n",
    "\n",
    "ax2.plot(x, t.sf(x), label='T (3)')\n",
    "ax2.plot(x, gp.sf(x), label='GenPareto (3)')\n",
    "ax2.plot(x, pareto.sf(x), label='Pareto (3)')\n",
    "\n",
    "ax2.scatter(\n",
    "    x[convergence], \n",
    "    t.sf(x[convergence]), \n",
    "    c='C3', marker='x', alpha=1,\n",
    "    label='Convergence'\n",
    ")\n",
    "\n",
    "ax2.set_xscale('log')\n",
    "ax2.set_yscale('log')\n",
    "\n",
    "ax2.set_ylabel('Log P(X>x)', loc='top', rotation='horizontal')\n",
    "ax2.set_xlabel('Log x', loc='right')\n",
    "\n",
    "ax2.legend()\n",
    "\n",
    "ax2.grid(False)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "+ meanwhile, the LogPareto is not only scale invariant at large $k$, it is also invariant to $n$!!! Or at least it tends there over time. This means as $\\alpha\\to0$ as $x\\to\\infty$, which can be seen below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "tags": [
     "hide_input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.ticker as mticks\n",
    "\n",
    "alpha = 2\n",
    "L = 1\n",
    "pareto = scist.pareto(alpha, scale=L)\n",
    "lp = ph.dists.LogPareto(alpha=alpha, L=L)\n",
    "x = np.linspace(1, 100,10000)\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(10,6))\n",
    "\n",
    "with np.errstate(divide='ignore'):\n",
    "    with warnings.catch_warnings():\n",
    "        warnings.simplefilter(\"ignore\")\n",
    "        ax.plot(x, pareto.sf(x)*np.exp(alpha), label='Pareto (2)')\n",
    "        ax.plot(x, lp.sf(x), label='Logpareto (2)')\n",
    "\n",
    "ax.set_xscale('log')\n",
    "ax.set_yscale('log')\n",
    "yticks = 10**np.arange(-3,3).astype('float')\n",
    "ax.set_yticks(yticks)\n",
    "ax.set_yticklabels(1/yticks[3:-3])\n",
    "ax.set_ylim((10**-3, 10**3))\n",
    "\n",
    "ax.xaxis.set_major_formatter(mticks.StrMethodFormatter('{x:.0f}'))\n",
    "ax.yaxis.set_major_formatter(mticks.StrMethodFormatter('{x:.2f}'))\n",
    "\n",
    "ax.set_ylabel('P(X>x)', loc='top', rotation='horizontal')\n",
    "ax.set_xlabel('x', loc='right')\n",
    "\n",
    "ax.legend()\n",
    "ax.grid(False)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Six Sigma is Not Six Sigma ##\n",
    "\n",
    "The impact of fat tails is readily observable in daily equity returns. In a Gaussian distribtion, a \"Six Sigma\" event (i.e. one that is 6 standard deviations from the mean) [should occur](https://arxiv.org/pdf/1103.5672.pdf) two in every  $10^9$ samples. For daily equity returns, this translates into a Six Sigma event occuring ***every ~4 million years***. By contrast, a Six Sigma event in the Pareto should occur once every ***36 days***."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Guassian: 4,022,201 years\n",
      "Pareto: 36 days\n"
     ]
    }
   ],
   "source": [
    "n_years_gauss = (1 / scist.norm.sf(6)) / 252\n",
    "n_days_pareto = (1/scist.pareto(2).sf(6))\n",
    "print (f'Guassian: {n_years_gauss:,.0f} years')\n",
    "print (f'Pareto: {n_days_pareto:.0f} days')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We are fed Black-Sholes and Guassian-based volatility for option pricing for much of our lives. And yet if you are just 10 years old, you've lived long enough to see a Six Sigma event in the US equity market. And if you've lived 80 years, well ... \n",
    "\n",
    "Below we show the occurrences of Six Sigma events in the S&P 500 over various timeframes. Each time the blue line breaches the red dotted line, that is a 2-in-4M year occurence according to the Gaussian."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[*********************100%***********************]  1 of 1 completed\n"
     ]
    }
   ],
   "source": [
    "import yfinance as yf\n",
    "\n",
    "sp = yf.download('^GSPC')\n",
    "sp_ret = sp.Close.pct_change()[1:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1296x1008 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from datetime import datetime as dt\n",
    "\n",
    "fig, axs = plt.subplots(2,2, figsize=(18,14))\n",
    "axs = axs.flatten()\n",
    "\n",
    "rngs = np.arange(30, 0, -10)\n",
    "rngs = np.concatenate(([90], rngs))\n",
    "titles = [f'Sigma over {rng} Year TimeFrames' for rng in rngs]\n",
    "for i in range(4):\n",
    "    sp_ret.plot(ax=axs[i])\n",
    "\n",
    "    yrs = np.arange(sp_ret.index.min().year, sp_ret.index.max().year, rngs[i])\n",
    "    yrs = np.array([dt(yr, 1, 1) for yr in yrs])\n",
    "\n",
    "    ranges = np.vstack((yrs[:-1], yrs[1:])).T\n",
    "\n",
    "    stds = []\n",
    "    for rng in ranges:\n",
    "        sp_split = sp_ret[slice(*rng)]\n",
    "        mean, std = scist.norm.fit(sp_split)\n",
    "        stds.append(std)\n",
    "\n",
    "    cum = np.concatenate((np.zeros(1), np.repeat(1 / len(stds), len(stds)).cumsum()))\n",
    "    trng = np.vstack((cum[:-1], cum[1:])).T\n",
    "    for j in range(len(stds)):\n",
    "        sig = axs[i].axhline(stds[j]*6, *trng[j], c='C3', ls='--', lw=1, label=r'$6\\sigma$')\n",
    "        signeg = axs[i].axhline(-stds[j]*6, *trng[j], c='C3', ls='--', lw=1, label=r'$-6\\sigma$')\n",
    "\n",
    "    axs[i].set_xlabel('')\n",
    "    axs[i].set_ylabel('Daily Returns')\n",
    "    axs[i].legend(handles=[sig])\n",
    "    axs[i].set_title(titles[i])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To paraphrase Taleb:\n",
    "\n",
    "> If you see a 6 sigma event, that's not a 6 sigma event.\n",
    "\n",
    "Daily equity returns are clearly ***not*** Gaussian, which has one major implication: Geometric Brownian Motion is not appropriate for share prices and by extension the Black-Scholes pricing model is utterly invalid. "
   ]
  }
 ],
 "metadata": {
  "celltoolbar": "Edit Metadata",
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.9.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}