[ENH] Alpha distribution (#356)

#### What does this implement/fix? Explain your changes.
<!--
A clear and concise description of what you have implemented.
--> Implements Alpha Distribution. Towards #22

docs/source/api_reference/distributions.rst

@@ -35,6 +35,7 @@ Continuous support
     :toctree: auto_generated/
     :template: class.rst
 
+    Alpha
     Beta
     ChiSquared
     Exponential

skpro/distributions/__init__.py

@@ -4,6 +4,7 @@
 # adapted from sktime
 
 __all__ = [
+    "Alpha",
     "Beta",
     "ChiSquared",
     "Delta",
@@ -28,6 +29,7 @@
     "Weibull",
 ]
 
+from skpro.distributions.alpha import Alpha
 from skpro.distributions.beta import Beta
 from skpro.distributions.chi_squared import ChiSquared
 from skpro.distributions.compose import IID

skpro/distributions/alpha.py

@@ -0,0 +1,79 @@
+# copyright: skpro developers, BSD-3-Clause License (see LICENSE file)
+"""Alpha probability distribution."""
+
+__author__ = ["SaiReavanth25"]
+
+import pandas as pd
+from scipy.stats import alpha, rv_continuous
+
+from skpro.distributions.adapters.scipy import _ScipyAdapter
+
+
+class Alpha(_ScipyAdapter):
+    r"""Alpha distribution.
+
+    The alpha distribution is characterized by its shape parameter :math:`\a`,
+    which determines its skewness and tail behavior.
+    It is often used for modeling data with heavy right tails,
+    unlike the Gaussian distribution(which is symmetric and bell-shaped).
+
+    The probability density function (PDF) of the Alpha distribution is given by:
+    .. math::
+
+        f(x) = \frac{1}{x^2 \Phi(a) \sqrt{2\pi}}
+                \exp\left(-\frac{1}{2}\left(\frac{a - 1}{x}\right)^2\right)
+
+    where:
+       - :math:`a` is the shape parameter.
+       - :math:`Phi` is the cumulative distribution function (CDF) of the
+                    standard normal distribution.
+
+
+    Parameters
+    ----------
+    a : float or array of float (1D or 2D), must be positive
+        Shape parameter controlling skewness and tail behavior.
+        Higher values result in heavier tails and greater skewness towards the right.
+    index : pd.Index, optional, default = RangeIndex
+    columns : pd.Index, optional, default = RangeIndex
+
+    Example
+    -------
+    >>> from skpro.distributions import Alpha
+
+    >>> distr = Alpha(a=[[1, 2], [3, 4]])
+    """
+
+    _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, a, index=None, columns=None):
+        self.a = a
+
+        super().__init__(index=index, columns=columns)
+
+    def _get_scipy_object(self) -> rv_continuous:
+        return alpha
+
+    def _get_scipy_param(self):
+        a = self._bc_params["a"]
+
+        return [a], {}
+
+    @classmethod
+    def get_test_params(cls, parameter_set="default"):
+        """Return testing parameter settings for the estimator."""
+        params1 = {"a": [[2, 3], [4, 5]]}
+        params2 = {
+            "a": 3,
+            "index": pd.Index([1, 2, 3]),
+            "columns": pd.Index(["a", "b"]),
+        }
+        params3 = {"a": 2.5}
+
+        return [params1, params2, params3]