[ENH] Half Cauchy Distribution (#371)

Implements Half Cauchy Distribution, towards #22

docs/source/api_reference/distributions.rst

@@ -41,6 +41,7 @@ Continuous support
     Exponential
     Fisk
     Gamma
+    HalfCauchy
     HalfNormal
     Laplace
     Logistic

skpro/distributions/__init__.py

@@ -12,6 +12,7 @@
     "Exponential",
     "Fisk",
     "Gamma",
+    "HalfCauchy",
     "HalfNormal",
     "IID",
     "Laplace",
@@ -39,6 +40,7 @@
 from skpro.distributions.exponential import Exponential
 from skpro.distributions.fisk import Fisk
 from skpro.distributions.gamma import Gamma
+from skpro.distributions.halfcauchy import HalfCauchy
 from skpro.distributions.halfnormal import HalfNormal
 from skpro.distributions.laplace import Laplace
 from skpro.distributions.logistic import Logistic

skpro/distributions/halfcauchy.py

@@ -0,0 +1,79 @@
+# copyright: skpro developers, BSD-3-Clause License (see LICENSE file)
+"""Half-Cauchy probability distribution."""
+
+__author__ = ["SaiRevanth25"]
+
+import pandas as pd
+from scipy.stats import halfcauchy, rv_continuous
+
+from skpro.distributions.adapters.scipy import _ScipyAdapter
+
+
+class HalfCauchy(_ScipyAdapter):
+    r"""Half-Cauchy distribution.
+
+    This distribution is univariate, without correlation between dimensions
+    for the array-valued case.
+
+    The half-Cauchy distribution is a continuous probability distribution that
+    is the positive half of the Cauchy distribution. It is commonly used in
+    Bayesian statistics, especially as a prior distribution for scale parameters
+    due to its heavy tails and non-negativity.
+
+    The half-Cauchy distribution is parametrized by the scale parameter
+    :math:`\beta`, such that the pdf is
+
+    .. math::
+
+        f(x) = \frac{2}{\pi \beta \left(1 + \left(\frac{x}{\beta}\right)^2\right)},
+                x>0 otherwise 0
+
+    The scale parameter :math:`\beta` is represented by the parameter ``beta``.
+
+    Parameters
+    ----------
+    beta : float or array of float (1D or 2D), must be positive
+        scale parameter of the half-Cauchy distribution
+    index : pd.Index, optional, default = RangeIndex
+    columns : pd.Index, optional, default = RangeIndex
+
+    Example
+    -------
+    >>> from skpro.distributions.halfcauchy import HalfCauchy
+
+    >>> hc = HalfCauchy(beta=1)
+    """
+
+    _tags = {
+        "capabilities:approx": ["pdfnorm"],
+        "capabilities:exact": ["mean", "var", "pdf", "log_pdf", "cdf", "ppf"],
+        "distr:measuretype": "continuous",
+        "distr:paramtype": "parametric",
+        "broadcast_init": "on",
+    }
+
+    def __init__(self, beta, index=None, columns=None):
+        self.beta = beta
+
+        super().__init__(index=index, columns=columns)
+
+    def _get_scipy_object(self) -> rv_continuous:
+        return halfcauchy
+
+    def _get_scipy_param(self):
+        beta = self._bc_params["beta"]
+        return [beta], {}
+
+    @classmethod
+    def get_test_params(cls, parameter_set="default"):
+        """Return testing parameter settings for the estimator."""
+        # array case examples
+        params1 = {"beta": [[1, 2], [3, 4]]}
+        params2 = {
+            "beta": 1,
+            "index": pd.Index([1, 2, 5]),
+            "columns": pd.Index(["a", "b"]),
+        }
+        # scalar case examples
+        params3 = {"beta": 2}
+        return [params1, params2, params3]