EVT Analysis.ipynb

{
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  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.stats import skewnorm, genpareto"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "real = torch.load('data/real.pt')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "sums = real.sum(dim=(1, 2, 3)).detach().cpu().numpy() / 4096"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "percentile = (100*(1-(0.75**10)))\n",
    "tail = np.where(sums > np.percentile(sums, percentile))[0][-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "body_dist, tail_dist = sums[tail:], sums[:tail]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "skewnorm_params = skewnorm.fit(sums)\n",
    "genpareto_params = genpareto.fit(tail_dist - sums[tail])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "body_rv = skewnorm(*skewnorm_params)\n",
    "tail_rv = genpareto(*genpareto_params)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.scatter(body_dist, body_rv.pdf(body_dist))\n",
    "plt.scatter(tail_dist, (1-body_rv.cdf(sums[tail]))*tail_rv.pdf(tail_dist - sums[tail]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.scatter(body_dist, body_rv.cdf(body_dist))\n",
    "plt.scatter(tail_dist, body_rv.cdf(body_dist[0])+(1-percentile)*tail_rv.cdf(tail_dist - sums[tail]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "sums[tail]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "genpareto_params"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "skewnorm_params"
   ]
  }
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