notebooks/demo-lambertw-f-distributions.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "d83ec1ad-f627-4d6f-b202-cd780921e976",
   "metadata": {},
   "source": [
    "# Demo of Lambert W x F distributions in torch\n",
    "\n",
    "This notebook illustrates the implementation of the Lambert W x F distributions using `torch` and `torch.distributions.Distribution` objects.\n",
    "\n",
    "This is based on work in \n",
    "\n",
    "\n",
    "Goerg (2011). Lambert W random variables—a new family of generalized skewed distributions with applications to risk estimation. Ann. Appl. Stat. 5 (3) 2197 - 2230, 2011. https://doi.org/10.1214/11-AOAS457\n",
    "\n",
    "Goerg (2015) The Lambert Way to Gaussianize Heavy-Tailed Data with the Inverse of Tukey’s h Transformation as a Special Case. The Scientific World Journal. Volume 2015 | Article ID 909231 | https://doi.org/10.1155/2015/909231\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "42eb4be5-7c2d-4e7e-9f6f-139f496614ec",
   "metadata": {},
   "outputs": [],
   "source": [
    "%load_ext autoreload\n",
    "%autoreload 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "2777ac7e-9ec3-493f-827e-336caf99df59",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Only run if not already on PYTHONPATH / venv\n",
    "import os\n",
    "import sys\n",
    "import pathlib\n",
    "from os.path import dirname\n",
    "parent_path = dirname(pathlib.Path(pathlib.Path(os.getcwd())))\n",
    "\n",
    "if parent_path not in sys.path:\n",
    "    sys.path.insert(0, parent_path)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "04b249c8-54ad-4dc4-99e6-88771cfdb67e",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import torch\n",
    "import scipy.special\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "\n",
    "import torchlambertw as tlw\n",
    "import torchlambertw.special\n",
    "from torchlambertw import distributions as tlwd"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8b7ebf11-4e8c-42f6-b937-de01352f77e0",
   "metadata": {},
   "source": [
    "## Lambert W x Gaussian\n",
    "\n",
    "\n",
    "Here is an illustration of a heavy-tail Lambert W x Gaussian distribution, which takes a Gaussian input and turns it into something heavy-tailed. If `tailweight = 0` then its just a Gaussian again.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "3c5d0428-b48a-43d3-bdd5-5a4a67e24c5f",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(TailLambertWNormal(tailweight: 0.25),\n",
       " torchlambertw.distributions.Normal.TailLambertWNormal,\n",
       " True)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Use a slightly heavy-tailed distribution with a tail parameter of 0.25 (ie moments < 1/0.25 = 4 exist).\n",
    "m = tlwd.TailLambertWNormal(loc=1.0, scale=3.0, tailweight=0.25)\n",
    "m, type(m), isinstance(m, torch.distributions.Distribution)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "781a8e6a-4b2b-4354-a946-bd8da20d363e",
   "metadata": {},
   "source": [
    "This is a `torch.distributions.Distributions` object; thus it has all the usual supported methods of distributions like sampling (`.sample()`), probability evaluation (`.log_prob()`), and moments (`.mean`, `.mode`, `.variance`, ...)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "f1607514-de90-4a74-b898-e92ba871bc24",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([7.2207, 0.1102])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "torch.manual_seed(0)\n",
    "m.sample((2,)) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "a1fb307c-31bb-44eb-a292-f94ebf962bcb",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor(0.2500) Real() tensor(1.) tensor(25.4558)\n"
     ]
    }
   ],
   "source": [
    "print(m.tailweight, m.support, m.mean, m.variance)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "3b1aa810-677a-429a-aac9-f0688b16938e",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: ylabel='Count'>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "y = m.sample((1000,)).numpy().ravel()\n",
    "\n",
    "sns.histplot(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "ad015d56-129e-4fda-ad6e-d1092d493c4c",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>loglik</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>normal</th>\n",
       "      <td>-3075.827637</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>normal_again</th>\n",
       "      <td>-3075.827637</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>lambertw_normal</th>\n",
       "      <td>-2869.566895</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                      loglik\n",
       "normal          -3075.827637\n",
       "normal_again    -3075.827637\n",
       "lambertw_normal -2869.566895"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# assume its normal and eval likelihood\n",
    "norm = torch.distributions.Normal(loc=y.mean(), scale=y.std())\n",
    "# Set tailweight = 0 ('delta' in the papers), then a Lambert W x Normal is identical to Normal\n",
    "norm_again = tlwd.TailLambertWNormal(loc=y.mean(), scale=y.std(), tailweight=0.0)\n",
    "\n",
    "# Compare likelihood of all three distributions; since data was generated from `m`, should have highest likelihood.\n",
    "def _loglik(dist, data):\n",
    "    return dist.log_prob(torch.tensor(data)).sum().numpy().ravel()[0]\n",
    "                         \n",
    "total_logliks = pd.Series(\n",
    "    {\"normal\": _loglik(norm, y),\n",
    "     \"normal_again\": _loglik(norm_again, y),\n",
    "     \"lambertw_normal\": _loglik(m, y)})\n",
    "total_logliks.plot()\n",
    "total_logliks.to_frame(\"loglik\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d8719a81-ad56-412b-88ca-7330ec45ea2e",
   "metadata": {
    "tags": []
   },
   "source": [
    "# Skewed Lambert W x F distributions\n",
    "\n",
    "For introducting skewness one can use the skewed Lambert W x F distributions; particularly\n",
    "interesting are skewed Lambert W x Gaussian distributions as they can be used to transform Normal data to skewed data (and back)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "c80ad7b4-4ae0-4b4f-a793-a15283829a60",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: ylabel='Count'>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "torch.manual_seed(0)\n",
    "m = tlwd.SkewLambertWNormal(loc=1.0, scale=3.0, skewweight=0.25)\n",
    "y = m.sample((1000,)).numpy().ravel()\n",
    "\n",
    "sns.histplot(y)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "78b51e41-3633-4e97-b1c7-a4f4093688ce",
   "metadata": {},
   "source": [
    "## Skewed Lambert W x Exponential distributions\n",
    "\n",
    "Lambert W x F distribution can be generated for any arbitratry F.  Here we show an example of a skewed Lambert W x Exponential distribution. For `skewweight > 0` , this will be more (right) skewed than a baseline exponential distribution. \n",
    "\n",
    "See Goerg (2011) and Kaarik et al. (2023)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "2c137b8d-5827-4f1b-bf55-6fcc1cf41ea7",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean: theoretical 0.520833; empirical: 0.481116\n"
     ]
    }
   ],
   "source": [
    "torch.manual_seed(0)\n",
    "m = tlwd.SkewLambertWExponential(rate=3.0, skewweight=0.2)\n",
    "y = m.sample((1000,)).numpy().ravel()\n",
    "print(\"mean: theoretical %f; empirical: %f\" % (m.mean.numpy(), np.mean(y)))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "db4be3a5-5e93-4383-a0f8-d40d705a1e21",
   "metadata": {},
   "source": [
    "Mean is larger than the 1/3. rate of the baseline exponential distribution because of the longer tail, which is also clearly visible in density chart and qqplot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "0bb9814e-8662-4c46-b3e9-d5eed22a0f28",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: ylabel='Count'>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.histplot(y)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1574df0b-7580-4139-b68c-1a534d8a5e80",
   "metadata": {},
   "source": [
    "# DIY: Create your own Lambert W x F distribution\n",
    "\n",
    "You can use Lambert W x F distribution by using the general purpose `TailLambertWDistribution` class that accepts any input distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "047e220e-c84d-4625-b7c6-445f463379a5",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "lw_norm = torchlambertw.distributions.TailLambertWNormal(\n",
    "    loc=0., scale=1., tailweight=0.3\n",
    ")\n",
    "\n",
    "lw_dist = torchlambertw.distributions.TailLambertWDistribution(\n",
    "    base_distribution=torch.distributions.Normal,\n",
    "    base_dist_args={\"loc\": 0.0, \"scale\": 0.1},\n",
    "    tailweight=0.3)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "ad80ed04-850e-41d9-bdec-43562d66e5a4",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1000,)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "torch.manual_seed(0)\n",
    "\n",
    "x = lw_dist.sample((1000,)).numpy()\n",
    "x.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "1d71b25d-47fa-4569-b3f9-512335a30b9e",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: ylabel='Proportion'>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.ecdfplot(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "ec8e6c52-81c1-49b0-9905-a0c5cb3fd546",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: ylabel='Count'>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYUAAAD4CAYAAAAD6PrjAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjcuNCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8WgzjOAAAACXBIWXMAAAsTAAALEwEAmpwYAAATv0lEQVR4nO3df5Bdd33e8feDtLJkyVgi3rqu5KncsYepS1vIKK4TZzrEThuHUOwwxjGTGkMUPA2EmMLE2KEdpn8wQ1pIoJC6o7EpCvXYGGJqBxyIazvxZCbYkY0D/gGNSuIgj0GborsgIYFW+vSPvXt8kXetu+u999zd+37NaPaeH/eex5LnPnvO9/xIVSFJEsBL2g4gSRodloIkqWEpSJIaloIkqWEpSJIaa9sO8GKcccYZtX379rZjSNKK8sgjj/xdVU3Ot2xFl8L27dvZs2dP2zEkaUVJ8vRCyzx8JElqWAqSpIalIElqWAqSpIalIElqWAqSpIalIElqDKwUknw8yf4kj/fM+y9JvpbkK0k+m2Rzz7Ibk+xN8vUkPzeoXJKkhQ1yT+ETwKUnzLsXeEVV/TPg/wA3AiQ5H7gK+Cfd9/y3JGsGmG3sVRUHDhzA52lI6jWwUqiqB4HvnDDvj6tqpjv5JWBb9/VlwO1V9YOq+mtgL3DBoLIJOp0OV33oLjqdTttRJI2QNscUfgX4o+7rrcA3e5bt6857niTXJtmTZM/U1NSAI65uExs2tR1B0ohppRSSvBeYAW5d7HuraldV7aiqHZOT897PSZK0REO/IV6SNwOvBS6p5w5oPwOc3bPatu48SdIQDXVPIcmlwPXA66rq+z2L7gauSnJKknOA84CHh5lNkjTAPYUktwGvBs5Isg94H7NnG50C3JsE4EtV9e+q6okkdwBPMntY6e1VdWxQ2SRJ8xtYKVTVG+eZfcsLrP9+4P2DyiNJOjmvaJYkNSwFSVLDUpAkNSwFSVLDUpAkNSwFSVLDUpAkNSwFSVLDUpAkNSwFSVLDUpAkNSwFSVLDUpAkNSwFSVLDUpAkNSwFSVLDUpAkNSwFSVLDUpAkNSwFSVLDUpAkNSwFSVLDUpAkNda2HUDDVVV0Oh06nU7bUSSNIEthzHQ6Ha6+6X6OHj5IJta3HUfSiBnY4aMkH0+yP8njPfNeluTeJH/V/bmlOz9J/muSvUm+kuTHB5VLsG7DJibWb2w7hqQRNMgxhU8Al54w7wbgvqo6D7ivOw3w88B53T/XAjcNMJckaQEDK4WqehD4zgmzLwN2d1/vBi7vmf/7NetLwOYkZw0qmyRpfsM+++jMqnq2+/pbwJnd11uBb/ast687T5I0RK2dklpVBdRi35fk2iR7kuyZmpoaQDJJGl/DLoVvzx0W6v7c353/DHB2z3rbuvOep6p2VdWOqtoxOTk50LCSNG6GXQp3A9d0X18D3NUz/03ds5AuBKZ7DjNJkoZkYNcpJLkNeDVwRpJ9wPuADwB3JNkJPA1c2V39HuA1wF7g+8BbBpVLkrSwgZVCVb1xgUWXzLNuAW8fVBYtrKo4cOAAAJs3byZJy4kktckrmsfc9PQ077jtUQA++WsXs2XLlpYTSWqTpSDWbdjUdgRJI8K7pEqSGpaCJKlhKYyxqmJ6errtGJJGiKUwxmaOHOK63Q8yc+xY21EkjQhLYcyt9RbaknpYCpKkhqUgSWpYCpKkhqUgSWpYCpKkhqUgSWpYCpKkhqUgSWpYCpKkhqUgSWpYCpKkhqUgSWpYCpKkhqUgSWpYCpKkhqUgSWpYCpKkhqUgSWpYCpKkRiulkOTfJ3kiyeNJbkuyPsk5SR5KsjfJp5KsayObJI2zoZdCkq3AbwA7quoVwBrgKuC3gd+tqnOBA8DOYWeTpHHX1uGjtcCGJGuBU4FngYuBz3SX7wYubyeaJI2voZdCVT0DfBD4W2bLYBp4BOhU1Ux3tX3A1vnen+TaJHuS7JmamhpGZEkaG20cPtoCXAacA/wDYCNwab/vr6pdVbWjqnZMTk4OKKUkjac2Dh/9LPDXVTVVVUeBO4GLgM3dw0kA24BnWsgmSWOtjVL4W+DCJKcmCXAJ8CTwAHBFd51rgLtayCZJY62NMYWHmB1QfhT4ajfDLuA9wLuS7AV+DLhl2NkkadytPfkqy6+q3ge874TZ3wAuaCGOJKnLK5olSQ1LQZLUsBQkSQ1LQQBUFZ1Oh6pqO4qkFlkKAuDo4YO8ddf9dDqdtqNIapGloMbaDZvajiCpZZaCJKlhKUiSGpaCJKlhKUiSGn2VQpKL+pmn0TZ32qkkLaTfPYWP9jlPI6zT6bDzY/cwc+xY21EkjagXvCFekp8EfgqYTPKunkUvZfbZylphJjZsbDuCpBF2srukrgM2ddc7rWf+d3nu2QeSpFXiBUuhqv4U+NMkn6iqp4eUSZLUkn6fp3BKkl3A9t73VNXFgwglSWpHv6XwaeC/AzcDjlJK0irVbynMVNVNA00iSWpdv6ek/mGStyU5K8nL5v4MNJkkaej63VO4pvvzN3vmFfCPljeOJKlNfZVCVZ0z6CCSpPb1VQpJ3jTf/Kr6/eWNI0lqU7+Hj36i5/V64BLgUcBSkKRVpN/DR+/onU6yGbh9EIEkSe1Z6q2zDwGOM0jSKtPvmMIfMnu2EczeCO8fA3csdaPdPY2bgVd0P/dXgK8Dn2L2qum/Aa6sqgNL3YYkafH6HVP4YM/rGeDpqtr3Irb7EeALVXVFknXAqcBvAfdV1QeS3ADcALznRWxDkrRIfR0+6t4Y72vM3il1C/DDpW4wyenAvwRu6X72D6uqA1wG7O6uthu4fKnbkCQtTb9PXrsSeBh4A3Al8FCSpd46+xxgCvgfSb6c5OYkG4Ezq+rZ7jrfAs5cIMu1SfYk2TM1NbXECJKk+fQ70Pxe4Ceq6pqqehNwAfAfl7jNtcCPAzdV1auYHbS+oXeFqiqeG8PghGW7qmpHVe2YnJxcYgRJ0nz6LYWXVNX+nun/t4j3nmgfsK+qHupOf4bZkvh2krMAuj/3L/B+SdKA9PvF/oUkX0zy5iRvBj4P3LOUDVbVt4BvJnl5d9YlwJPA3Tx3j6VrgLuW8vmSpKU72TOaz2X2WP9vJnk98NPdRX8O3PoitvsO4NbumUffAN7CbEHdkWQn8DSzYxeSpCE62SmpHwZuBKiqO4E7AZL80+6yf7OUjVbVY8COeRZdspTPkyQtj5MdPjqzqr564szuvO0DSaTWVBWdTofZcX5J4+hkpbD5BZZtWMYcGgEzRw7x1l330+l02o4iqSUnK4U9Sd564swkvwo8MphIatPaDZvajiCpRScbU3gn8Nkkv8xzJbADWAf84gBzSZJa8IKlUFXfBn4qyc8we/M6gM9X1f0DTyZJGrp+n6fwAPDAgLNIklq21KuSJUmrkKUwJuZON5WkF2IpjIlOp8POj93DzLFjbUeRNMIshTEysWFj2xEkjThLQZLUsBQkSQ1LQZLUsBQkSQ1LQZLUsBQkSQ1LQZLU6OveR1q55q5k9mpmSf2wFFa5TqfD1Tfdz9HDB72aWdJJefhoDKzbsImJ9V7NLOnkLAVJUsNSkCQ1LAVJUsNSkCQ1LAVJUqO1UkiyJsmXk3yuO31OkoeS7E3yqSTr2somSeOqzT2F64CneqZ/G/jdqjoXOADsbCWVJI2xVkohyTbgF4Cbu9MBLgY+011lN3B5G9kkaZy1tafwYeB64Hh3+seATlXNdKf3AVvne2OSa5PsSbJnampq4EElaZwMvRSSvBbYX1WPLOX9VbWrqnZU1Y7JycllTidJ462Nex9dBLwuyWuA9cBLgY8Am5Os7e4tbAOeaSGbJI21oe8pVNWNVbWtqrYDVwH3V9UvAw8AV3RXuwa4a9jZJGncjdJ1Cu8B3pVkL7NjDLe0nEeSxk6rt86uqj8B/qT7+hvABW3mkaRxN0p7CpKkllkKkqSGpbCKzT2KU5L6ZSmsYp1Oh50fu8fHcErqm6Wwyk1sWNpjOKuKAwcOUFXLnEjSKLMUNK9Op8NVH7rLw0/SmLEUtKCJDZvajiBpyFq9TkGjx8FpabxZCvoRM0cO8bZPPszxo0fIxPq240gaMktBzzNx6mkc/8Eaz1qSxpBjCpKkhqUgSWpYCpKkhqUgSWpYCpKkhqUgSWpYCpKkhqUgSWpYCpKkhqUgSWpYCpKkhqUgSWpYCpKkhqUgSWpYCpKkxtBLIcnZSR5I8mSSJ5Jc153/siT3Jvmr7s8tw84mSeOujT2FGeDdVXU+cCHw9iTnAzcA91XVecB93WlJ0hANvRSq6tmqerT7+nvAU8BW4DJgd3e13cDlw84mSeOu1TGFJNuBVwEPAWdW1bPdRd8Czmwr12pQVXQ6nbZjSFphWiuFJJuAPwDeWVXf7V1WVQXUAu+7NsmeJHumpqaGkHRl6nQ67PzYPT5nWdKitFIKSSaYLYRbq+rO7uxvJzmru/wsYP98762qXVW1o6p2TE5ODifwCjWxYWPbESStMG2cfRTgFuCpqvqdnkV3A9d0X18D3DXsbJI07ta2sM2LgKuBryZ5rDvvt4APAHck2Qk8DVzZQjZJGmtDL4Wq+jMgCyy+ZJhZJEk/yiuataC5M5hmx/0ljQNLQQuaOXKIt+6631NbpTFiKegFrd2wqe0IkobIUpAkNdo4+0grSO+V0Zs3b2b2jGJJq5V7CnpBM0cO8bZPPszVNzm2II0D9xRWkd6zhZbzC3zi1NNYu2bNsn2epNFlKawinU6Hq2+6n6OHD3Lk4DRr13ubC0mLYymsMus2bIIqZmZm2o4iaQVyTEF98UI2aTxYCurL0cMHvZBNGgOWgvrmhWzS6mcprBLDeNKah5Ck1c9SWCWG8aQ174UkrX6WwioyjCeteQhJWt0sBUlSw1LQovSOK1QVBw4ccIxBWkUsBS1K77hCp9Phqg/d5RiDtIpYClq03nGFCccYpFXFUliBPGwjaVAshRXIwzaSBsUb4q1QvYdthnHhWq+Tbe/Ei9y2bNniw3mkFcJSWAXmLlzLuvWcMoTtzT145/jRI2Ri/bx55m7hfWxmhk9f/3q2bNkyhGSSXixLYYQs9OjLufmnn34609PTzTpzYwudToeJDRsHejXziSZOPY3jP1iz4DbnbuGdIWaS9OJZCiOg98v9N27/MgCf/LWLm9+uO50Ov/TB/8V/fsOr+A/3/F+OHj5IJtYzPT3NO257lKOHDw61EObLPneoqKqYnp5+wfU7nY7Pe5ZGlKUwAjqdDle8/zaOHT/G6VvPnffRl0m4bveDnL71XCaqmhJoHqpzcOEv4kGaOXKIt3z0c5y65UyOHz3CkW6O07eeO+/6c4Pkt7/7Mg8pSSNo5EohyaXAR4A1wM1V9YHl3sZCh2mWa/0T33vgwAGAH/nN/8TPmdiwsTnU0vvbd+8X56g+XnPt+o3PHU6a54lvvf89nU6Htes3NtNJBr7XcOLeybD2Vnr/7ec46D5cq23P9MV8F/VrpEohyRrg94B/BewD/iLJ3VX15HJuZ24gFH70MM1yrX/ie694/228ZN16Pn396wFO+pvy0cMHectHP8fE+o3Ne1ay3sNcc8+Ontu7WLN27aL/ThfrxL2TYe2tzP3bn3L6GRw/esRB9xastj3TF/Nd1K+RKgXgAmBvVX0DIMntwGXAspZCr35O5exdZ7Gnfi703hNfHz18iGPHj3H0+9/j+NEjz1vvxOXHZmaYnp7mh4cPcvTIIWaOHJpdr7t8bnq+eS92ejHvmcvZq/dzTvy7GIS5z1/o56C3e7J5Gpxh/VsPyzD+OzJKV8UmuQK4tKp+tTt9NfAvqurXe9a5Fri2O/ly4OtDD/p8ZwB/13aIJTL78K3U3GD2Ngwi9z+sqsn5FozansJJVdUuYFfbOXol2VNVO9rOsRRmH76VmhvM3oZh5x6121w8A5zdM72tO0+SNASjVgp/AZyX5Jwk64CrgLtbziRJY2OkDh9V1UySXwe+yOwpqR+vqidajtWPkTqctUhmH76VmhvM3oah5h6pgWZJUrtG7fCRJKlFloIkqWEpLJMkb0jyRJLjSUb+tLcklyb5epK9SW5oO89iJPl4kv1JHm87y2IkOTvJA0me7P6/cl3bmfqVZH2Sh5P8ZTf7f2o702IkWZPky0k+13aWxUjyN0m+muSxJHuGsU1LYfk8DrweeLDtICfTczuRnwfOB96Y5Px2Uy3KJ4BL2w6xBDPAu6vqfOBC4O0r6O/9B8DFVfXPgVcClya5sN1Ii3Id8FTbIZboZ6rqlcO6VsFSWCZV9VRVjcLV1f1obidSVT8E5m4nsiJU1YPAd9rOsVhV9WxVPdp9/T1mv6S2tpuqPzXrYHdyovtnRZylkmQb8AvAzW1nWQkshfG0Ffhmz/Q+VsiX02qRZDvwKuChlqP0rXsI5jFgP3BvVa2U7B8GrgeOt5xjKQr44ySPdG/xM3AjdZ3CqEvyv4G/P8+i91bVXcPOo5UpySbgD4B3VtV3287Tr6o6BrwyyWbgs0leUVUjPa6T5LXA/qp6JMmrW46zFD9dVc8k+XvAvUm+1t1THhhLYRGq6mfbzrBMvJ1IS5JMMFsIt1bVnW3nWYqq6iR5gNlxnZEuBeAi4HVJXgOsB16a5H9W1b9tOVdfquqZ7s/9ST7L7KHfgZaCh4/Gk7cTaUFmn4hyC/BUVf1O23kWI8lkdw+BJBuYfebJ11oN1YequrGqtlXVdmb/P79/pRRCko1JTpt7DfxrhlDClsIySfKLSfYBPwl8PskX2860kKqaAeZuJ/IUcMcKuZ0IAEluA/4ceHmSfUl2tp2pTxcBVwMXd08xfKz7G+xKcBbwQJKvMPtLxb1VtaJO71yBzgT+LMlfAg8Dn6+qLwx6o97mQpLUcE9BktSwFCRJDUtBktSwFCRJDUtBktSwFCRJDUtBktT4/5EmInvrJeZRAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.histplot(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b6d03857-9eac-454f-8264-bb49aca75427",
   "metadata": {},
   "source": [
    "## Generate a Lambert W x Weibull distribution\n",
    "\n",
    "See also `distributions.SkewLambertWWeibull` and `distributions.TailLambertWWeibull`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "5735a165-31de-4e6a-9514-22a1c69218df",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "weibull_args = {\"concentration\": 3., \"scale\": 10.}\n",
    "input_distr = torch.distributions.Weibull(**weibull_args)\n",
    "\n",
    "def _plot_distr(distr, ax=None):\n",
    "    \n",
    "    x = np.sort(distr.sample((5000, )).numpy())\n",
    "    pdf = np.exp(distr.log_prob(torch.tensor(x))).numpy()\n",
    "    plt.plot(x, pdf, axes=ax)\n",
    "    plt.grid()\n",
    "    \n",
    "_plot_distr(input_distr)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "id": "ac635141-a157-4b77-8db2-1f5f5af7724c",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "tail_lw_weib = torchlambertw.distributions.TailLambertWDistribution(\n",
    "    base_distribution=torch.distributions.Weibull,\n",
    "    base_dist_args=weibull_args,\n",
    "    use_mean_variance=True,\n",
    "    tailweight=0.1)\n",
    "\n",
    "skew_lw_weib = torchlambertw.distributions.SkewLambertWDistribution(\n",
    "    base_distribution=torch.distributions.Weibull,\n",
    "    base_dist_args=weibull_args,\n",
    "    use_mean_variance=True,\n",
    "    skewweight=0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "id": "3fa672c1-a813-495a-9d0a-c0bfc26cd1ca",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f39abddb1c0>"
      ]
     },
     "execution_count": 113,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "torch.manual_seed(11)\n",
    "\n",
    "fig, ax = plt.subplots(1,1, facecolor=(1, 1, 1))\n",
    "_plot_distr(input_distr, ax=ax)\n",
    "_plot_distr(tail_lw_weib, ax=ax)\n",
    "_plot_distr(skew_lw_weib, ax=ax)\n",
    "plt.grid()\n",
    "plt.legend([\"Weibull\", \"Tail Lambert W x Weibull\", \"Skew Lambert W x Weibull\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5caea172-44d2-4ed9-8da5-0a3befd4f11a",
   "metadata": {},
   "source": [
    "### Likelihood evaluation as a function of tailweight\n",
    "\n",
    "Fixing true parameters at *known* values, consider the `log_prob()` likelihood as a function of tailweight."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "id": "65703395-9d7d-4a1e-936f-bbc8f95d610d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<seaborn.axisgrid.FacetGrid at 0x7f39ab4834c0>"
      ]
     },
     "execution_count": 114,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "xx = skew_lw_weib.sample([1000]).numpy()\n",
    "sns.displot(xx)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "id": "1aa89dc2-208d-4ce8-aff5-6a39dd09034e",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "loglik = {}\n",
    "for g in np.linspace(0., 1., num=101):\n",
    "    # Use the built-in SkewLambertWWeibull distribution.\n",
    "    skew_lw_weib = torchlambertw.distributions.SkewLambertWWeibull(\n",
    "        **weibull_args,\n",
    "        use_mean_variance=True,\n",
    "        skewweight=g)\n",
    "    loglik[g] = float(skew_lw_weib.log_prob(torch.tensor(xx)).mean().numpy())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "id": "20be41f0-b518-4053-9922-88227dd06440",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pd.Series(loglik).plot()\n",
    "plt.ylabel(\"average log-likelihood\")\n",
    "plt.xlabel(\"skewweight (gamma) parameter\")\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "id": "1ff2cd2b-3814-49d7-8992-108c2b012a7b",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.22"
      ]
     },
     "execution_count": 118,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.Series(loglik).idxmax()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c63373b4-8906-441b-aec6-5e80c230ed80",
   "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": "3.8.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}