[ENH] Logistic distribution (#241)

Towards #22

#### What does this implement/fix? Explain your changes.
Logistic probability distribution

.all-contributorsrc

@@ -129,6 +129,15 @@
       "contributions": [
         "code"
       ]
+    },
+    {
+      "login": "malikrafsan",
+      "name": "Malik Akbar Hashemi Rafsanjani",
+      "avatar_url": "https://avatars.githubusercontent.com/u/77711133?v=4",
+      "profile": "https://github.com/malikrafsan",
+      "contributions": [
+        "code"
+      ]
     }
   ]
 }

docs/source/api_reference/distributions.rst

@@ -36,6 +36,7 @@ Continuous support
     :template: class.rst
 
     Laplace
+    Logistic
     Normal
     TDistribution
     Weibull

skpro/distributions/__init__.py

@@ -5,9 +5,10 @@
 __all__ = [
     "Empirical",
     "Laplace",
+    "Logistic",
+    "LogNormal",
     "Mixture",
     "Normal",
-    "LogNormal",
     "Poisson",
     "QPD_S",
     "QPD_B",
@@ -18,6 +19,7 @@
 
 from skpro.distributions.empirical import Empirical
 from skpro.distributions.laplace import Laplace
+from skpro.distributions.logistic import Logistic
 from skpro.distributions.lognormal import LogNormal
 from skpro.distributions.mixture import Mixture
 from skpro.distributions.normal import Normal

skpro/distributions/logistic.py

@@ -0,0 +1,122 @@
+# copyright: skpro developers, BSD-3-Clause License (see LICENSE file)
+"""Logistic probability distribution."""
+
+__author__ = ["malikrafsan"]
+
+import numpy as np
+import pandas as pd
+
+from skpro.distributions.base import BaseDistribution
+
+
+class Logistic(BaseDistribution):
+    """Logistic distribution.
+
+    Parameters
+    ----------
+    mu : float or array of float (1D or 2D)
+        mean of the logistic distribution
+    scale : float or array of float (1D or 2D), must be positive
+        scale parameter of the distribution
+    index : pd.Index, optional, default = RangeIndex
+    columns : pd.Index, optional, default = RangeIndex
+
+    Example
+    -------
+    >>> from skpro.distributions.logistic import Logistic
+
+    >>> l = Logistic(mu=[[0, 1], [2, 3], [4, 5]], scale=1)
+    """
+
+    _tags = {
+        "capabilities:approx": ["pdfnorm", "energy"],
+        "capabilities:exact": ["mean", "var", "pdf", "log_pdf", "cdf", "ppf"],
+        "distr:measuretype": "continuous",
+    }
+
+    def __init__(self, mu, scale, index=None, columns=None):
+        self.mu = mu
+        self.scale = scale
+        self.index = index
+        self.columns = columns
+
+        # todo: untangle index handling
+        # and broadcast of parameters.
+        # move this functionality to the base class
+        self._mu, self._scale = self._get_bc_params(self.mu, self.scale)
+        shape = self._mu.shape
+
+        if index is None:
+            index = pd.RangeIndex(shape[0])
+
+        if columns is None:
+            columns = pd.RangeIndex(shape[1])
+
+        super().__init__(index=index, columns=columns)
+
+    def mean(self):
+        r"""Return expected value of the distribution.
+
+        Let :math:`X` be a random variable with the distribution of `self`.
+        Returns the expectation :math:`\mathbb{E}[X]`
+
+        Returns
+        -------
+        pd.DataFrame with same rows, columns as `self`
+        expected value of distribution (entry-wise)
+        """
+        mean_arr = self._mu
+        return pd.DataFrame(mean_arr, index=self.index, columns=self.columns)
+
+    def var(self):
+        r"""Return variance of the distribution.
+
+        Let :math:`X` be a random variable with the distribution of `self`.
+        Returns the variance :math:`\mathbb{V}[X] = \frac{\mathbb{S}^2 \times \pi^3}{3}`
+
+        Returns
+        -------
+        pd.DataFrame with same rows, columns as `self`
+        variance of distribution (entry-wise)
+        """
+        var_arr = (self._scale**2 * np.pi**2) / 3
+        return pd.DataFrame(var_arr, index=self.index, columns=self.columns)
+
+    def pdf(self, x):
+        """Probability density function."""
+        d = self.loc[x.index, x.columns]
+        numerator = np.exp(-(x.values - d.mu) / d.scale)
+        denominator = d.scale * ((1 + np.exp(-(x.values - d.mu) / d.scale)) ** 2)
+        pdf_arr = numerator / denominator
+        return pd.DataFrame(pdf_arr, index=x.index, columns=x.columns)
+
+    def log_pdf(self, x):
+        """Logarithmic probability density function."""
+        d = self.loc[x.index, x.columns]
+        y = -(x.values - d.mu) / d.scale
+        lpdf_arr = y - np.log(d.scale) - 2 * np.logaddexp(0, y)
+        return pd.DataFrame(lpdf_arr, index=x.index, columns=x.columns)
+
+    def cdf(self, x):
+        """Cumulative distribution function."""
+        d = self.loc[x.index, x.columns]
+        cdf_arr = (1 + np.tanh((x.values - d.mu) / (2 * d.scale))) / 2
+        return pd.DataFrame(cdf_arr, index=x.index, columns=x.columns)
+
+    def ppf(self, p):
+        """Quantile function = percent point function = inverse cdf."""
+        d = self.loc[p.index, p.columns]
+        ppf_arr = d.mu + d.scale * np.log(p.values / (1 - p.values))
+        return pd.DataFrame(ppf_arr, index=p.index, columns=p.columns)
+
+    @classmethod
+    def get_test_params(cls, parameter_set="default"):
+        """Return testing parameter settings for the estimator."""
+        params1 = {"mu": [[0, 1], [2, 3], [4, 5]], "scale": 1}
+        params2 = {
+            "mu": 0,
+            "scale": 1,
+            "index": pd.Index([1, 2, 5]),
+            "columns": pd.Index(["a", "b"]),
+        }
+        return [params1, params2]