Update pymc.HalfStudentT docsting (#5555)

* fixed pymc.HalfStudentT docsting

* added :context: close-figs and removed sd from dist

* undo the sd change

pymc/distributions/continuous.py

@@ -2691,7 +2691,7 @@ def rng_fn(cls, rng, nu, sigma, size=None) -> np.ndarray:
 
 class HalfStudentT(PositiveContinuous):
     r"""
-    Half Student's T log-likelihood
+    Half Student's T log-likelihood.
 
     The pdf of this distribution is
 
@@ -2703,6 +2703,7 @@ class HalfStudentT(PositiveContinuous):
             \left(1+\frac{1}{\nu}\frac{x^2}{\sigma^2}\right)^{-\frac{\nu+1}{2}}
 
     .. plot::
+        :context: close-figs
 
         import matplotlib.pyplot as plt
         import numpy as np
@@ -2726,14 +2727,14 @@ class HalfStudentT(PositiveContinuous):
 
     Parameters
     ----------
-    nu: float
+    nu : tensor_like of float, default 1
         Degrees of freedom, also known as normality parameter (nu > 0).
-    sigma: float
+    sigma : tensor_like of float, optional
         Scale parameter (sigma > 0). Converges to the standard deviation as nu
-        increases. (only required if lam is not specified)
-    lam: float
+        increases (only required if lam is not specified). Defaults to 1.
+    lam : tensor_like of float, optional
         Scale parameter (lam > 0). Converges to the precision as nu
-        increases. (only required if sigma is not specified)
+        increases (only required if sigma is not specified). Defaults to 1.
 
     Examples
     --------
@@ -2776,9 +2777,9 @@ def logp(value, nu, sigma):
 
         Parameters
         ----------
-        value: numeric
+        value : tensor_like of float
             Value(s) for which log-probability is calculated. If the log probabilities for multiple
-            values are desired the values must be provided in a numpy array or Aesara tensor
+            values are desired the values must be provided in a numpy array or Aesara tensor.
 
         Returns
         -------