[ENH] Erlang Distribution (#518)

#### Reference Issues/PRs

Implementing a distribution towards #22 

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

Implements Erlang Distribution

docs/source/api_reference/distributions.rst

@@ -55,6 +55,7 @@ Continuous support - non-negative reals
     Beta
     ChiSquared
     Exponential
+    Erlang
     Fisk
     Gamma
     HalfCauchy

skpro/distributions/__init__.py

@@ -10,6 +10,7 @@
     "ChiSquared",
     "Delta",
     "Empirical",
+    "Erlang",
     "Exponential",
     "Fisk",
     "Gamma",
@@ -46,6 +47,7 @@
 from skpro.distributions.compose import IID
 from skpro.distributions.delta import Delta
 from skpro.distributions.empirical import Empirical
+from skpro.distributions.erlang import Erlang
 from skpro.distributions.exponential import Exponential
 from skpro.distributions.fisk import Fisk
 from skpro.distributions.gamma import Gamma

skpro/distributions/erlang.py

@@ -0,0 +1,80 @@
+# copyright: skpro developers, BSD-3-Clause License (see LICENSE file)
+"""Erlang probability distribution."""
+
+__author__ = ["RUPESH-KUMAR01"]
+
+import pandas as pd
+from scipy.stats import erlang
+
+from skpro.distributions.adapters.scipy import _ScipyAdapter
+
+
+class Erlang(_ScipyAdapter):
+    r"""Erlang Distribution.
+
+    Most methods wrap ``scipy.stats.erlang``.
+
+    The Erlang Distribution is parameterized by shape :math:`k`
+    and rate :math:`\lambda`, such that the pdf is
+
+    .. math:: f(x) = \frac{x^{k-1}\exp\left(-\lambda x\right) \lambda^{k}}{(k-1)!}
+
+    Parameters
+    ----------
+    rate : float or array of float (1D or 2D)
+        Represents the rate parameter, which is also the inverse of the scale parameter.
+    k : int or array of int (1D or 2D), optional, default = 1
+        Represents the shape parameter.
+    index : pd.Index, optional, default = RangeIndex
+    columns : pd.Index, optional, default = RangeIndex
+
+    Examples
+    --------
+    >>> from skpro.distributions.erlang import Erlang
+
+    >>> d = Erlang(rate=[[1, 1], [2, 3], [4, 5]], shape=2)
+    """
+
+    _tags = {
+        "capabilities:approx": ["energy", "pdfnorm"],
+        "capabilities:exact": ["mean", "var", "pdf", "log_pdf", "cdf", "ppf"],
+        "distr:measuretype": "continuous",
+        "distr:paramtype": "parametric",
+        "broadcast_init": "on",
+    }
+
+    def __init__(self, rate, k=1, index=None, columns=None):
+        if rate <= 0:
+            raise ValueError("Rate must be greater than 0.")
+        if k <= 0:
+            raise ValueError("shape must be a positive integer.")
+        self.rate = rate
+        self.k = k
+
+        super().__init__(index=index, columns=columns)
+
+    def _get_scipy_object(self):
+        return erlang
+
+    def _get_scipy_param(self):
+        rate = self._bc_params["rate"]
+        k = self._bc_params["k"]
+
+        return [], {"scale": 1 / rate, "a": k}
+
+    @classmethod
+    def get_test_params(cls, parameter_set="default"):
+        """Return testing parameter settings for the estimator."""
+        # Array case examples
+        params1 = {
+            "rate": 2.0,
+            "k": 3,
+            "index": pd.Index([0, 1, 2]),
+            "columns": pd.Index(["x", "y"]),
+        }
+        # Scalar case examples
+        params2 = {"rate": 0.8, "k": 2}
+
+        params3 = {"rate": 3.0, "k": 1}
+
+        return [params1, params2, params3]