Add docstring for `HalfCauchyRV`

aesara/tensor/random/basic.py

@@ -1036,6 +1036,18 @@ cauchy = CauchyRV()
 
 
 class HalfCauchyRV(ScipyRandomVariable):
+    r"""A half-Cauchy continuous random variable.
+
+    The probability density function for `halfcauchy` in terms of its location
+    parameter :math:`x_0` and scale parameter :math:`\gamma` is:
+
+    .. math::
+
+        f(x; x_0, \gamma) = \frac{1}{\pi \gamma \left(1 + (\frac{x-x_0}{\gamma})^2\right)}
+
+    for :math:`x \geq 0` where :math:`\gamma > 0`.
+
+    """
     name = "halfcauchy"
     ndim_supp = 0
     ndims_params = [0, 0]
@@ -1043,6 +1055,21 @@ class HalfCauchyRV(ScipyRandomVariable):
     _print_name = ("C**+", "\\operatorname{C^{+}}")
 
     def __call__(self, loc=0.0, scale=1.0, size=None, **kwargs):
+        r"""Draw samples from a half-Cauchy distribution.
+
+        Parameters
+        ----------
+        loc
+            Location parameter :math:`x_0` of the distribution.
+        scale
+            Scale parameter :math:`\gamma` of the distribution. Must be
+            positive.
+        size
+           Sample shape. If the given size is `(m, n, k)`, then `m * n * k`
+           independent, identically distributed samples are returned. Default is
+           `None`, in which case a single sample is returned.
+
+        """
         return super().__call__(loc, scale, size=size, **kwargs)
 
     @classmethod

doc/library/tensor/random/basic.rst

@@ -73,6 +73,9 @@ Aesara can produce :class:`RandomVariable`\s that draw samples from many differe
 .. autoclass:: aesara.tensor.random.basic.GumbelRV
    :members: __call__
 
+.. autoclass:: aesara.tensor.random.basic.HalfCauchyRV
+   :members: __call__
+
 .. autoclass:: aesara.tensor.random.basic.HalfNormalRV
    :members: __call__