examples/03_skpro_distributions.ipynb

{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## skpro probability distributions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Set-up instructions:** On binder, this should run out-of-the-box.\n",
    "\n",
    "To run locally instead, ensure that `skpro` with basic dependency requirements is installed in your python environment."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`skpro` provides a unified interface to probability distributions, with an API that:\n",
    "\n",
    "* is `scikit-learn` and `scikit-base` compliant, parametric objects with `get_params`, `set_params`\n",
    "* allows to represent data frame and 2D arrays of distributions easily, as return objects in `predict_proba`\n",
    "* is `pandas` copmliant, with `index`, `columns`, indexing and subsetting via `iloc`, `loc`\n",
    "* provides easy access to informative and didactic vicualizations via `matplotlib`\n",
    "\n",
    "**Section 1** provides an **overview of core API elements**\n",
    "\n",
    "**Section 2** gives an overview of **distribution object methods**, relevant tags and configs\n",
    "\n",
    "**Section 3** introduces **composite distributions** and related APIs\n",
    "\n",
    "**Section 4** gives an introduction to writing API compliant **custom probability distributions**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# hide warnings\n",
    "import warnings\n",
    "\n",
    "warnings.filterwarnings(\"ignore\")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. `skpro` probability distributions <a class=\"anchor\" id=\"chapter1\"></a>"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.1 probability distributions base interface"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`skpro` distributions are parametric objects:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
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See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-e27d3995-2a1e-4b86-ac6d-a910daae9c84 div.sk-text-repr-fallback {display: none;}</style><div id='sk-e27d3995-2a1e-4b86-ac6d-a910daae9c84' class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>Normal(mu=1, sigma=2)</pre><b>Please rerun this cell to show the HTML repr or trust the notebook.</b></div><div class=\"sk-container\" hidden><div class='sk-item'><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=UUID('23f92ef2-30f2-4a57-b2ca-4f24c31b55e4') type=\"checkbox\" checked><label for=UUID('23f92ef2-30f2-4a57-b2ca-4f24c31b55e4') class='sk-toggleable__label sk-toggleable__label-arrow'>Normal</label><div class=\"sk-toggleable__content\"><pre>Normal(mu=1, sigma=2)</pre></div></div></div></div></div>"
      ],
      "text/plain": [
       "Normal(mu=1, sigma=2)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from skpro.distributions import Normal\n",
    "\n",
    "# defining a normal distribution with mean 1 and std 2\n",
    "n = Normal(mu=1, sigma=2)\n",
    "\n",
    "n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The object `n` is a symbolic representation of a normal distribution.\n",
    "\n",
    "The object provides various useful methods:\n",
    "\n",
    "* properties and functions such as `pdf`, `cdf`, `mean`, `var`\n",
    "* a method to sample from the distribution, `sample`\n",
    "* a method to visualize the distribution, `plot`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='x', ylabel='pdf(x)'>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n.plot(\"pdf\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.17603266338214976"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# evaluate the pdf, compare the figure\n",
    "n.pdf(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# mean/expectation of the distribution\n",
    "# same as mu, for normal\n",
    "n.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# variance of the distribution\n",
    "# same as sigma-squared, for normal\n",
    "n.var()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='x', ylabel='cdf(x)'>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the cdf\n",
    "n.plot(\"cdf\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n.cdf(1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "the `sample` method can be used to produce a single independent sample, or multiple:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7275802027978109"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# produce single sample\n",
    "n.sample()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "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>0</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.493892</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.386263</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-0.026326</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-1.435938</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>3.775277</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>3.869872</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.568660</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>-1.495968</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0.442317</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>-1.776917</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          0\n",
       "0  0.493892\n",
       "1  0.386263\n",
       "2 -0.026326\n",
       "3 -1.435938\n",
       "4  3.775277\n",
       "5  3.869872\n",
       "6  0.568660\n",
       "7 -1.495968\n",
       "8  0.442317\n",
       "9 -1.776917"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# produce an i.i.d. sample of size 10\n",
    "n.sample(10)\n",
    "# returned as a pd.DataFrame"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "parameters can be set and accessed via `get_params`, `set_params` - like in `scikit-learn`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'columns': None, 'index': None, 'mu': 1, 'sigma': 2}"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n.get_params()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.2 DataFrame-like distributions, array distributions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`skpro` distributions are designed to easily represent DataFrame-like distributions,\n",
    "\n",
    "i.e., array distributions with row (instance) index and column (variable) index\n",
    "\n",
    "all distributions can be constructed as a DataFrame-like distribution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "from skpro.distributions import Normal\n",
    "\n",
    "instance_names = [1, 2, 3]\n",
    "variable_names = [\"foo\", \"bar\"]\n",
    "\n",
    "# the syntax is similar to pandas:\n",
    "# parameters passed as arrays\n",
    "# index, columns passed\n",
    "\n",
    "mus = [[1, 2], [2, 3], [3, 4]]\n",
    "sigmas = [[1, 1], [2, 1], [1, 2]]\n",
    "n = Normal(mu=mus, sigma=sigmas, index=instance_names, columns=variable_names)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`n` represents a joint distribution of independent normals in an array, with row and column index\n",
    "\n",
    "(most) methods behave as applying array input to marginals\n",
    "\n",
    "e.g., visualisation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(<Figure size 640x480 with 6 Axes>,\n",
       " array([[<Axes: title={'center': 'foo'}, ylabel='1'>,\n",
       "         <Axes: title={'center': 'bar'}>],\n",
       "        [<Axes: ylabel='2'>, <Axes: >],\n",
       "        [<Axes: ylabel='3'>, <Axes: >]], dtype=object))"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n.plot(\"cdf\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(<Figure size 640x480 with 6 Axes>,\n",
       " array([[<Axes: title={'center': 'foo'}, ylabel='1'>,\n",
       "         <Axes: title={'center': 'bar'}>],\n",
       "        [<Axes: ylabel='2'>, <Axes: >],\n",
       "        [<Axes: ylabel='3'>, <Axes: >]], dtype=object))"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n.plot(\"pdf\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "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>foo</th>\n",
       "      <th>bar</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.503769</td>\n",
       "      <td>0.915566</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3.765281</td>\n",
       "      <td>4.262243</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2.294784</td>\n",
       "      <td>1.104473</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        foo       bar\n",
       "1  1.503769  0.915566\n",
       "2  3.765281  4.262243\n",
       "3  2.294784  1.104473"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# sampling produces DataFrame with same index, columns\n",
    "n.sample()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "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>foo</th>\n",
       "      <th>bar</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   foo  bar\n",
       "1    1    2\n",
       "2    2    3\n",
       "3    3    4"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# same for mean\n",
    "n.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "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>foo</th>\n",
       "      <th>bar</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   foo  bar\n",
       "1    1    1\n",
       "2    4    1\n",
       "3    1    4"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# variance\n",
    "n.var()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "methods with arguments broadcast to 2D"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "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>foo</th>\n",
       "      <th>bar</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.398942</td>\n",
       "      <td>0.241971</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.176033</td>\n",
       "      <td>0.053991</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.053991</td>\n",
       "      <td>0.064759</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        foo       bar\n",
       "1  0.398942  0.241971\n",
       "2  0.176033  0.053991\n",
       "3  0.053991  0.064759"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# methods with arguments broadcast\n",
    "n.pdf(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "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>foo</th>\n",
       "      <th>bar</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.398942</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.176033</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.053991</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        foo  bar\n",
       "1  0.398942  0.0\n",
       "2  0.176033  0.0\n",
       "3  0.053991  0.0"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 1D is considered as a row when broadcasting\n",
    "n.pdf([1, 100])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "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>foo</th>\n",
       "      <th>bar</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.398942</td>\n",
       "      <td>0.241971</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.199471</td>\n",
       "      <td>0.241971</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        foo       bar\n",
       "1  0.398942  0.241971\n",
       "2  0.199471  0.241971\n",
       "3  0.000000  0.000000"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# to broadcast column-wise, use 2D column vector\n",
    "n.pdf([[1], [2], [100]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "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>foo</th>\n",
       "      <th>bar</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.398942</td>\n",
       "      <td>0.398942</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.176033</td>\n",
       "      <td>0.053991</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.053991</td>\n",
       "      <td>0.064759</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        foo       bar\n",
       "1  0.398942  0.398942\n",
       "2  0.176033  0.053991\n",
       "3  0.053991  0.064759"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 2D is evaluated entry-wise\n",
    "n.pdf([[1, 2], [3, 5], [5, 7]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`skpro` distribution objects are pandas-like!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3, 2)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`index` and `columns` are coerced to `pandas.Index` subtypes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index([1, 2, 3], dtype='int64')"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n.index"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['foo', 'bar'], dtype='object')"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n.columns  # same columns as X_new"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "subsetting with `iloc` (integer location) and `loc` works as in `pandas`:\n",
    "\n",
    "* `iloc[rows, cols]` and `loc[rows, cols]` subset to an array distribution\n",
    "* `iat[row, col]` and `at[row, col]` subset to a scalar distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(<Figure size 640x480 with 2 Axes>,\n",
       " array([<Axes: title={'center': 'bar'}, ylabel='1'>, <Axes: ylabel='3'>],\n",
       "       dtype=object))"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# we wubset to two rows and one column\n",
    "n_subset = n.iloc[[0, 2], [1]]\n",
    "# n_subset.shape = (2, 1)\n",
    "n_subset.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(<Figure size 640x480 with 2 Axes>,\n",
       " array([<Axes: title={'center': 'bar'}, ylabel='1'>, <Axes: ylabel='3'>],\n",
       "       dtype=object))"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# same rows, cols, but with loc indexing\n",
    "n_subset = n.loc[[1, 3], [\"bar\"]]\n",
    "# n_subset.shape = (2, 1)\n",
    "n_subset.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-c2e0c789-a962-447b-b807-4b6cd10f98fe {color: black;background-color: white;}#sk-c2e0c789-a962-447b-b807-4b6cd10f98fe pre{padding: 0;}#sk-c2e0c789-a962-447b-b807-4b6cd10f98fe div.sk-toggleable {background-color: white;}#sk-c2e0c789-a962-447b-b807-4b6cd10f98fe label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-c2e0c789-a962-447b-b807-4b6cd10f98fe label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-c2e0c789-a962-447b-b807-4b6cd10f98fe label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-c2e0c789-a962-447b-b807-4b6cd10f98fe div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-c2e0c789-a962-447b-b807-4b6cd10f98fe div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-c2e0c789-a962-447b-b807-4b6cd10f98fe div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-c2e0c789-a962-447b-b807-4b6cd10f98fe input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-c2e0c789-a962-447b-b807-4b6cd10f98fe input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-c2e0c789-a962-447b-b807-4b6cd10f98fe div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-c2e0c789-a962-447b-b807-4b6cd10f98fe div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-c2e0c789-a962-447b-b807-4b6cd10f98fe input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-c2e0c789-a962-447b-b807-4b6cd10f98fe div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-c2e0c789-a962-447b-b807-4b6cd10f98fe div.sk-estimator:hover {background-color: #d4ebff;}#sk-c2e0c789-a962-447b-b807-4b6cd10f98fe div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-c2e0c789-a962-447b-b807-4b6cd10f98fe div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-c2e0c789-a962-447b-b807-4b6cd10f98fe div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 2em;bottom: 0;left: 50%;}#sk-c2e0c789-a962-447b-b807-4b6cd10f98fe div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;}#sk-c2e0c789-a962-447b-b807-4b6cd10f98fe div.sk-item {z-index: 1;}#sk-c2e0c789-a962-447b-b807-4b6cd10f98fe div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;}#sk-c2e0c789-a962-447b-b807-4b6cd10f98fe div.sk-parallel::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 2em;bottom: 0;left: 50%;}#sk-c2e0c789-a962-447b-b807-4b6cd10f98fe div.sk-parallel-item {display: flex;flex-direction: column;position: relative;background-color: white;}#sk-c2e0c789-a962-447b-b807-4b6cd10f98fe div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-c2e0c789-a962-447b-b807-4b6cd10f98fe div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-c2e0c789-a962-447b-b807-4b6cd10f98fe div.sk-parallel-item:only-child::after {width: 0;}#sk-c2e0c789-a962-447b-b807-4b6cd10f98fe div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;position: relative;}#sk-c2e0c789-a962-447b-b807-4b6cd10f98fe div.sk-label label {font-family: monospace;font-weight: bold;background-color: white;display: inline-block;line-height: 1.2em;}#sk-c2e0c789-a962-447b-b807-4b6cd10f98fe div.sk-label-container {position: relative;z-index: 2;text-align: center;}#sk-c2e0c789-a962-447b-b807-4b6cd10f98fe div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-c2e0c789-a962-447b-b807-4b6cd10f98fe div.sk-text-repr-fallback {display: none;}</style><div id='sk-c2e0c789-a962-447b-b807-4b6cd10f98fe' class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>Normal(mu=2.0, sigma=1.0)</pre><b>Please rerun this cell to show the HTML repr or trust the notebook.</b></div><div class=\"sk-container\" hidden><div class='sk-item'><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=UUID('74cc8ce5-92b5-4fbd-8398-ac98ec6cc372') type=\"checkbox\" checked><label for=UUID('74cc8ce5-92b5-4fbd-8398-ac98ec6cc372') class='sk-toggleable__label sk-toggleable__label-arrow'>Normal</label><div class=\"sk-toggleable__content\"><pre>Normal(mu=2.0, sigma=1.0)</pre></div></div></div></div></div>"
      ],
      "text/plain": [
       "Normal(mu=2.0, sigma=1.0)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# subsetting to a scalar distribution\n",
    "n.at[1, \"bar\"]\n",
    "# this behaves the same as the distribution in the previous section"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.3 DataFrame-like distributions - broadcasting"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "at construction, all (simple) probability distributions broadcast parameters:\n",
    "\n",
    "* if `index` or `columns` are passed, always broadcasts to 2D\n",
    "* 1D iterables are interpreted as row vectors, i.e., of shape (1, n)\n",
    "* if `index` and `columns` are absent, and the result is 2D, uses `RangeIndex` (integers starting at 0)\n",
    "* the result is a scalar distribution only if `index`, `columns` are not passed, and all parameters are zero-D (scalar)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3, 1)"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# broadcasting example: index is passed\n",
    "from skpro.distributions import Normal\n",
    "\n",
    "n = Normal(mu=1, sigma=2, index=[1, 2, 3])\n",
    "# results in a shape (3, 1) distribution, with all mu, sigma being 1, 2\n",
    "n.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "\n",
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       "\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
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       "      <th></th>\n",
       "      <th>0</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   0\n",
       "1  1\n",
       "2  1\n",
       "3  1"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
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       "    }\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>0</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   0\n",
       "1  4\n",
       "2  4\n",
       "3  4"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n.var()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2, 2)"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# broadcasting example: a parameter is non-scalar\n",
    "from skpro.distributions import Normal\n",
    "\n",
    "n = Normal(mu=[[1, 2], [2, 3]], sigma=2)\n",
    "# results in a shape (2, 2) distribution\n",
    "# sigma is broadcast to the shape of mu\n",
    "# index, columns are RangeIndex, i.e., [0, 1]\n",
    "n.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
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       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   0  1\n",
       "0  1  2\n",
       "1  2  3"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1, 3)"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# broadcasting example: 1D parameter is broadcast as a row\n",
    "from skpro.distributions import Normal\n",
    "\n",
    "n = Normal(mu=[1, 2, 3], sigma=2)\n",
    "# results in a shape (1, 3) distribution\n",
    "# mu is interpreted as (1, 3) row vector\n",
    "# sigma is broadcast to the shape of mu\n",
    "# index, columns are RangeIndex, i.e., index=[0] and columns=[0, 1, 2]\n",
    "n.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
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       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
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       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   0  1  2\n",
       "0  1  2  3"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n.mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.4 searching for probability distributions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "as first-class citizens, all objects in `skpro` are indexed via the `registry` utility `all_objects`.\n",
    "\n",
    "To find probabilisty distributions, use `all_objects` with the type `distribution`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "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>name</th>\n",
       "      <th>object</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Beta</td>\n",
       "      <td>&lt;class 'skpro.distributions.beta.Beta'&gt;</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>ChiSquared</td>\n",
       "      <td>&lt;class 'skpro.distributions.chi_squared.ChiSqu...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Delta</td>\n",
       "      <td>&lt;class 'skpro.distributions.delta.Delta'&gt;</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Empirical</td>\n",
       "      <td>&lt;class 'skpro.distributions.empirical.Empirical'&gt;</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Fisk</td>\n",
       "      <td>&lt;class 'skpro.distributions.fisk.Fisk'&gt;</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         name                                             object\n",
       "0        Beta            <class 'skpro.distributions.beta.Beta'>\n",
       "1  ChiSquared  <class 'skpro.distributions.chi_squared.ChiSqu...\n",
       "2       Delta          <class 'skpro.distributions.delta.Delta'>\n",
       "3   Empirical  <class 'skpro.distributions.empirical.Empirical'>\n",
       "4        Fisk            <class 'skpro.distributions.fisk.Fisk'>"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from skpro.registry import all_objects\n",
    "\n",
    "all_objects(\"distribution\", as_dataframe=True).head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "a full list can also be found in the online API reference."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "all tags can be printed by the `all_tags` utility:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "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>name</th>\n",
       "      <th>scitype</th>\n",
       "      <th>type</th>\n",
       "      <th>description</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>approx_energy_spl</td>\n",
       "      <td>distribution</td>\n",
       "      <td>int</td>\n",
       "      <td>sample size used in MC estimates of energy</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>approx_mean_spl</td>\n",
       "      <td>distribution</td>\n",
       "      <td>int</td>\n",
       "      <td>sample size used in MC estimates of mean</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>approx_spl</td>\n",
       "      <td>distribution</td>\n",
       "      <td>int</td>\n",
       "      <td>sample size used in other MC estimates</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>approx_var_spl</td>\n",
       "      <td>distribution</td>\n",
       "      <td>int</td>\n",
       "      <td>sample size used in MC estimates of var</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>bisect_iter</td>\n",
       "      <td>distribution</td>\n",
       "      <td>int</td>\n",
       "      <td>max iters for bisection method in ppf</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>broadcast_init</td>\n",
       "      <td>distribution</td>\n",
       "      <td>(str, [on, off])</td>\n",
       "      <td>whether to initialize broadcast parameters in ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>broadcast_inner</td>\n",
       "      <td>distribution</td>\n",
       "      <td>(str, [array, scalar])</td>\n",
       "      <td>if inner logic is vectorized ('array') or scal...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>broadcast_params</td>\n",
       "      <td>distribution</td>\n",
       "      <td>(list, str)</td>\n",
       "      <td>distribution parameters to broadcast, compleme...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>capabilities:approx</td>\n",
       "      <td>distribution</td>\n",
       "      <td>(list, str)</td>\n",
       "      <td>methods of distr that are approximate</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>capabilities:exact</td>\n",
       "      <td>distribution</td>\n",
       "      <td>(list, str)</td>\n",
       "      <td>methods of distr that are numerically exact</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>distr:measuretype</td>\n",
       "      <td>distribution</td>\n",
       "      <td>(str, [continuous, discrete, mixed])</td>\n",
       "      <td>measure type of distr</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>distr:paramtype</td>\n",
       "      <td>distribution</td>\n",
       "      <td>(str, [general, parametric, nonparametric, com...</td>\n",
       "      <td>parametrization type of distribution</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   name       scitype  \\\n",
       "0     approx_energy_spl  distribution   \n",
       "1       approx_mean_spl  distribution   \n",
       "2            approx_spl  distribution   \n",
       "3        approx_var_spl  distribution   \n",
       "4           bisect_iter  distribution   \n",
       "5        broadcast_init  distribution   \n",
       "6       broadcast_inner  distribution   \n",
       "7      broadcast_params  distribution   \n",
       "8   capabilities:approx  distribution   \n",
       "9    capabilities:exact  distribution   \n",
       "10    distr:measuretype  distribution   \n",
       "11      distr:paramtype  distribution   \n",
       "\n",
       "                                                 type  \\\n",
       "0                                                 int   \n",
       "1                                                 int   \n",
       "2                                                 int   \n",
       "3                                                 int   \n",
       "4                                                 int   \n",
       "5                                    (str, [on, off])   \n",
       "6                              (str, [array, scalar])   \n",
       "7                                         (list, str)   \n",
       "8                                         (list, str)   \n",
       "9                                         (list, str)   \n",
       "10               (str, [continuous, discrete, mixed])   \n",
       "11  (str, [general, parametric, nonparametric, com...   \n",
       "\n",
       "                                          description  \n",
       "0          sample size used in MC estimates of energy  \n",
       "1            sample size used in MC estimates of mean  \n",
       "2              sample size used in other MC estimates  \n",
       "3             sample size used in MC estimates of var  \n",
       "4               max iters for bisection method in ppf  \n",
       "5   whether to initialize broadcast parameters in ...  \n",
       "6   if inner logic is vectorized ('array') or scal...  \n",
       "7   distribution parameters to broadcast, compleme...  \n",
       "8               methods of distr that are approximate  \n",
       "9         methods of distr that are numerically exact  \n",
       "10                              measure type of distr  \n",
       "11               parametrization type of distribution  "
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# all tags applicable to probability distribution\n",
    "from skpro.registry import all_tags\n",
    "\n",
    "all_tags(\"distribution\", as_dataframe=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "filtering in search can be done with the `filter_tags` argument in `all_objects`, see docstring:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "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>name</th>\n",
       "      <th>object</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Beta</td>\n",
       "      <td>&lt;class 'skpro.distributions.beta.Beta'&gt;</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>ChiSquared</td>\n",
       "      <td>&lt;class 'skpro.distributions.chi_squared.ChiSqu...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Fisk</td>\n",
       "      <td>&lt;class 'skpro.distributions.fisk.Fisk'&gt;</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Laplace</td>\n",
       "      <td>&lt;class 'skpro.distributions.laplace.Laplace'&gt;</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>LogNormal</td>\n",
       "      <td>&lt;class 'skpro.distributions.lognormal.LogNormal'&gt;</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Logistic</td>\n",
       "      <td>&lt;class 'skpro.distributions.logistic.Logistic'&gt;</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>Normal</td>\n",
       "      <td>&lt;class 'skpro.distributions.normal.Normal'&gt;</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>QPD_B</td>\n",
       "      <td>&lt;class 'skpro.distributions.qpd.QPD_B'&gt;</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>QPD_S</td>\n",
       "      <td>&lt;class 'skpro.distributions.qpd.QPD_S'&gt;</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>QPD_U</td>\n",
       "      <td>&lt;class 'skpro.distributions.qpd.QPD_U'&gt;</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>TDistribution</td>\n",
       "      <td>&lt;class 'skpro.distributions.t.TDistribution'&gt;</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>Uniform</td>\n",
       "      <td>&lt;class 'skpro.distributions.uniform.Uniform'&gt;</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>Weibull</td>\n",
       "      <td>&lt;class 'skpro.distributions.weibull.Weibull'&gt;</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             name                                             object\n",
       "0            Beta            <class 'skpro.distributions.beta.Beta'>\n",
       "1      ChiSquared  <class 'skpro.distributions.chi_squared.ChiSqu...\n",
       "2            Fisk            <class 'skpro.distributions.fisk.Fisk'>\n",
       "3         Laplace      <class 'skpro.distributions.laplace.Laplace'>\n",
       "4       LogNormal  <class 'skpro.distributions.lognormal.LogNormal'>\n",
       "5        Logistic    <class 'skpro.distributions.logistic.Logistic'>\n",
       "6          Normal        <class 'skpro.distributions.normal.Normal'>\n",
       "7           QPD_B            <class 'skpro.distributions.qpd.QPD_B'>\n",
       "8           QPD_S            <class 'skpro.distributions.qpd.QPD_S'>\n",
       "9           QPD_U            <class 'skpro.distributions.qpd.QPD_U'>\n",
       "10  TDistribution      <class 'skpro.distributions.t.TDistribution'>\n",
       "11        Uniform      <class 'skpro.distributions.uniform.Uniform'>\n",
       "12        Weibull      <class 'skpro.distributions.weibull.Weibull'>"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from skpro.registry import all_objects\n",
    "\n",
    "# \"retrieve all absolutely continuous distributions on the reals\"\n",
    "all_objects(\n",
    "    \"distribution\", as_dataframe=True, filter_tags={\"distr:measuretype\": \"continuous\"}\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. probability distributions - methods <a class=\"anchor\" id=\"chapter2\"></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This section presents an overview of methods of probability distributions, with mathematical references.\n",
    "\n",
    "The section is separated into:\n",
    "\n",
    "* common properties and distribution defining functions, such as `pdf`, `cdf`\n",
    "* overview of tags, approximation configs\n",
    "* uncommon and exotic properties and functions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For simplicity, the methods are presented only "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.1 common distribution methods"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let $X$ be a random variable supported on the reals, with distribution represented by a (scalar) `skpro` distribution `d`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "from skpro.distributions import Normal\n",
    "\n",
    "d = Normal(mu=1, sigma=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following table lists common distribution methods with their meaning:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "| Method   | English | Mathematical  | Arguments |\n",
    "|----------|---|:-------------:|------|\n",
    "| `mean` | expectation | $\\mathbb{E}[X]$ | none |\n",
    "| `var` | variance | $\\mathbb{V}[X]$ | none |\n",
    "| `cdf` | cumulative distribution function | $F_X(x) = P(X\\le x)$ | `x`, for $x\\in \\mathbb{R}$ |\n",
    "| `ppf` | percent point function or inverse cdf | $F_X^{-1}(p)$ | `p`, for $p\\in [0, 1]$ |\n",
    "| `pdf` | probability density function | $p_X(x) = (dp/dx) (x)$ | `x`, for $x\\in \\mathbb{R}$ |\n",
    "| `pmf` | probability mass function | $m_X(x) = P(X = x)$ | `x`, for $x\\in \\mathbb{R}$ |"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`skpro` can represent (absolutely) continuous, discrete, and mixed distributions over the reals (without singular part). All distributions possess `pmf`, and `pdf`, as the uniquely defined discrete resp continuous parts of the measure."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`mean` and `var` compute mean and variance, without arguments:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1, 4)"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(d.mean(), d.var())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`ppf` takes arguments in the range of $[0,1]$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.0488010254160813"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d.ppf(0.7)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`cdf`, `pdf`, `pmf` take arguments on the domain of $X$, i.e., real numbers:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.5, 0.17603266338214976, array(0))"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(d.cdf(1), d.pdf(2), d.pmf(3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note: as the normal distribution is absolutely continuous, it has no discrete part, and `pmf` will always return 0."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "All methods can be displayed via `plot`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='x', ylabel='ppf(x)'>"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib.pyplot import subplots\n",
    "\n",
    "fig, ax = subplots(2, 2)\n",
    "\n",
    "d.plot(\"cdf\", ax=ax[0, 0])\n",
    "d.plot(\"pmf\", ax=ax[0, 1])\n",
    "d.plot(\"pdf\", ax=ax[1, 0])\n",
    "d.plot(\"ppf\", ax=ax[1, 1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As explained in section 1, all methods generalize to dataframe-like distributions and broadcast arguments, see there. For instance:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "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>0</th>\n",
       "      <th>1</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.691462</td>\n",
       "      <td>0.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.500000</td>\n",
       "      <td>0.308538</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.308538</td>\n",
       "      <td>0.158655</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          0         1\n",
       "0  0.691462  0.500000\n",
       "1  0.500000  0.308538\n",
       "2  0.308538  0.158655"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from skpro.distributions import Normal\n",
    "\n",
    "d_frame = Normal(mu=[[1, 2], [2, 3], [3, 4]], sigma=2)\n",
    "\n",
    "d_frame.cdf(2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.2 distribution tags and tag specific features"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "properties of distributions are also available as tags.\n",
    "\n",
    "The tag `\"distr:measuretype\"` indicates whether the distribution is absolutely continuous, discrete, or mixed:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'continuous'"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from skpro.distributions import Normal\n",
    "\n",
    "d = Normal(mu=1, sigma=2)\n",
    "d.get_tags()[\"distr:measuretype\"]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The tag `\"distr:paramtype\"` indicates whether the distribution is parametric, nonparametric, or composite:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'parametric'"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from skpro.distributions import Normal\n",
    "\n",
    "d = Normal(mu=1, sigma=2)\n",
    "d.get_tags()[\"distr:paramtype\"]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "parametric distributions can be converted to `DataFrame` based represeitations:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "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</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  mu sigma\n",
       "0  1     2"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# scalar distributions convert to a single row with parameter values\n",
    "d.to_df()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "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 tr th {\n",
       "        text-align: left;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th colspan=\"2\" halign=\"left\">var1</th>\n",
       "      <th colspan=\"2\" halign=\"left\">var2</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th>mu</th>\n",
       "      <th>sigma</th>\n",
       "      <th>mu</th>\n",
       "      <th>sigma</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>4</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>5</td>\n",
       "      <td>2</td>\n",
       "      <td>6</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  var1       var2      \n",
       "    mu sigma   mu sigma\n",
       "0    1     2    2     2\n",
       "1    3     2    4     2\n",
       "2    5     2    6     2"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# dataframe distributions convert to a DataFrame\n",
    "# with column MultiIndex (variable, parameter)\n",
    "d = Normal(mu=[[1, 2], [3, 4], [5, 6]], sigma=2, columns=[\"var1\", \"var2\"])\n",
    "d.to_df()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The tags `capabilities:exact` and `capabilities:approx` indicate which methods are numerically exact, or approximative.\n",
    "\n",
    "An approximative method may not be numerically exact, typically has lower accuracy or higher runtime.\n",
    "\n",
    "For instance, the method may be computed using Monte Carlo estimates, or numerical integration."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['mean', 'var', 'energy', 'pdf', 'log_pdf', 'cdf', 'ppf']"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d.get_tags()[\"capabilities:exact\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['pdfnorm']"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d.get_tags()[\"capabilities:approx\"]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.3 uncommon distribution methods"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This section lists further, uncommon distribution methods.\n",
    "\n",
    "Let $X$ be a random variable supported on the reals, with distribution represented by a (scalar) `skpro` distribution `d`.\n",
    "Let $Y$ be an i.i.d. copy of $X$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "| Method   | English | Mathematical  | Arguments |\n",
    "|----------|---|:-------------:|------|\n",
    "| `log_pdf` | logarithmic pdf | $\\log p_X(x)$ | `x`, for $x\\in \\mathbb{R}$ |\n",
    "| `log_pmf` | logarithmic pmf | $\\log m_X(x)$ | `x`, for $x\\in \\mathbb{R}$ |\n",
    "| `energy` | energy function | $\\mathbb{E}[\\|X - Y\\|]$ | none |\n",
    "| `energy` | energy function | $\\mathbb{E}[\\|X - x\\|]$ | `x`, for $x\\in \\mathbb{R}$ |\n",
    "| `pdfnorm` | `pdf` integral | $\\int p_X(x)^a \\; dx$ | `a`, for $a\\in \\mathbb{R}^+$ |"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`log_pdf`, `log_pmf` are logarithmic versions of `pdf`, `pmf`, with natural logarithm.\n",
    "\n",
    "These may be more accurate than taking logarithm of `pdf`, `pmf`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`energy` are energy expressions used for instance in computation of CRPS.\n",
    "\n",
    "If no argument is passed, the self-term is computed; if `x` is passed, the cross-term is computed."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "All the above behave similarly, all are plottable and available for array distributions.\n",
    "\n",
    "`energy` always returns a single column data frame in case of array distributions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-3.6120857137646176"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Example:\n",
    "from skpro.distributions import Normal\n",
    "\n",
    "d = Normal(mu=1, sigma=2)\n",
    "\n",
    "d.log_pdf(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='x', ylabel='log_pdf(x)'>"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "d.plot(\"log_pdf\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. composite probability distributions <a class=\"anchor\" id=\"chapter3\"></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "work in progress"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4. Extension guide - implementing your own probabilisty distribution <a class=\"anchor\" id=\"chapter4\"></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "`skpro` is meant to be easily extensible, for direct contribution to `skpro` as well as for local/private extension with custom methods.\n",
    "\n",
    "To get started:\n",
    "\n",
    "* Follow the [\"implementing estimator\" developer guide](https://skpro.readthedocs.io/en/stable/developer_guide/add_estimators.html)\n",
    "* Use the [probabilistic regressor template](https://github.com/sktime/skpro/blob/main/extension_templates/regression.py) to get started\n",
    "\n",
    "1. Read through the [probability distribution extension template](https://github.com/sktime/skpro/blob/main/extension_templates/distributions.py) - this is a `python` file with `todo` blocks that mark the places in which changes need to be added.\n",
    "2. Copy the distribution extension template to a local folder in your own repository (local/private extension), or to a suitable location in your clone of the `skpro` or affiliated repository (if contributed extension), inside `skpro.distributions`; rename the file and update the file docstring appropriately.\n",
    "3. Address the \"todo\" parts. Usually, this means: changing the name of the class, setting the tag values, specifying hyper-parameters, filling in `__init__`, and as many methods as possible, most importantly `_ppf`, and possibly other common methods such as `_pdf` or `_pmf`, `_cdf`. You can add private methods as long as they do not override the default public interface. For more details, see the extension template.\n",
    "4. To test your estimator manually: import your estimator and run it in the workflows in Section 1; then use it in the compositors in Section 3.\n",
    "5. To test your estimator automatically: call `skpro.utils.check_estimator` on your estimator. You can call this on a class or object instance. Ensure you have specified test parameters in the `get_test_params` method, according to the extension template.\n",
    "\n",
    "In case of direct contribution to `skpro` or one of its affiliated packages, additionally:\n",
    "\n",
    "* Add yourself as an author to the code, and to the `CODEOWNERS` for the new estimator file(s).\n",
    "* Create a pull request that contains only the new estimators (and their inheritance tree, if it's not just one class), as well as the automated tests as described above.\n",
    "* In the pull request, describe the estimator and optimally provide a publication or other technical reference for the strategy it implements.\n",
    "* Before making the pull request, ensure that you have all necessary permissions to contribute the code to a permissive license (BSD-3) open source project."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5. Summary<a class=\"anchor\" id=\"chapter5\"></a>\n",
    "\n",
    "* `skpro` provides a unified interface for probability distributions, with an interface inspired by `scikit-learn` and `pandas`\n",
    "\n",
    "* `skpro` distributions are parametric first class objects. They are symbolic representations of probability distribution, and come with methods such as `pdf`, `cdf`, `sample`, `plot`, etc\n",
    "\n",
    "* `skpro` distributions can be scalar-valued, or data frame valued. The latter broadcast parameters and arguments of methods to 2D, and are returned by `skpro` probabilistic regressors or survival regressors `predict_proba`\n",
    "\n",
    "* `skpro` is easy to extend, and comes with user friendly tools to facilitate implementing and testing your own probability distributions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "### Credits:\n",
    "\n",
    "noteook creation: fkiraly\n",
    "\n",
    "skpro: https://github.com/sktime/skpro/blob/main/CONTRIBUTORS.md"
   ]
  }
 ],
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