diff --git a/pymc/distributions/shape_utils.py b/pymc/distributions/shape_utils.py
index f85e5dc477..74f7ebbb6f 100644
--- a/pymc/distributions/shape_utils.py
+++ b/pymc/distributions/shape_utils.py
@@ -20,7 +20,7 @@
 import warnings
 
 from functools import singledispatch
-from typing import Any, Optional, Sequence, Tuple, Union, cast
+from typing import Any, Iterable, Optional, Sequence, Tuple, Union, cast
 
 import numpy as np
 
@@ -49,18 +49,28 @@
 from pymc.util import _add_future_warning_tag
 
 
-def to_tuple(shape):
-    """Convert ints, arrays, and Nones to tuples
+def to_tuple(shape: Optional[Union[None, int, np.ndarray]]) -> Tuple:
+    """Convert integers, arrays, and Nones to tuples.
 
     Parameters
     ----------
-    shape: None, int or array-like
-        Represents the shape to convert to tuple.
+    shape : None, int, or array-like
+        Represents the shape to convert to a tuple.
 
     Returns
     -------
-    If `shape` is None, returns an empty tuple. If it's an int, (shape,) is
-    returned. If it is array-like, tuple(shape) is returned.
+    tuple
+        If `shape` is None, returns an empty tuple. If it's an int, (shape,) is
+        returned. If it is array-like, `tuple(shape)` is returned.
+
+    Examples
+    --------
+    >>> to_tuple(None)
+    ()
+    >>> to_tuple(5)
+    (5,)
+    >>> to_tuple([1, 2, 3])
+    (1, 2, 3)
     """
     if shape is None:
         return tuple()
@@ -87,26 +97,27 @@ def _check_shape_type(shape):
     return tuple(out)
 
 
-def broadcast_dist_samples_shape(shapes, size=None):
-    """Apply shape broadcasting to shape tuples but assuming that the shapes
-    correspond to draws from random variables, with the `size` tuple possibly
-    prepended to it. The `size` prepend is ignored to consider if the supplied
-    `shapes` can broadcast or not. It is prepended to the resulting broadcasted
-    `shapes`, if any of the shape tuples had the `size` prepend.
+def broadcast_dist_samples_shape(
+    shapes: Iterable[Tuple[int, ...]], size: Optional[int] = None
+) -> Tuple[int, ...]:
+    """Apply shape broadcasting to shape tuples for random variables.
 
     Parameters
     ----------
-    shapes: Iterable of tuples holding the distribution samples shapes
-    size: None, int or tuple (optional)
-        size of the sample set requested.
+    shapes : Iterable of tuples
+        Tuples holding the distribution samples shapes.
+    size : None, int, or tuple, optional
+        Size of the sample set requested.
 
     Returns
     -------
-    tuple of the resulting shape
+    tuple
+        The resulting broadcasted shape.
 
     Examples
     --------
     .. code-block:: python
+
         size = 100
         shape0 = (size,)
         shape1 = (size, 5)
@@ -114,7 +125,9 @@ def broadcast_dist_samples_shape(shapes, size=None):
         out = broadcast_dist_samples_shape([shape0, shape1, shape2],
                                            size=size)
         assert out == (size, 4, 5)
+
     .. code-block:: python
+
         size = 100
         shape0 = (size,)
         shape1 = (5,)
@@ -122,7 +135,9 @@ def broadcast_dist_samples_shape(shapes, size=None):
         out = broadcast_dist_samples_shape([shape0, shape1, shape2],
                                            size=size)
         assert out == (size, 4, 5)
+
     .. code-block:: python
+
         size = 100
         shape0 = (1,)
         shape1 = (5,)
@@ -291,7 +306,18 @@ def find_size(
 
 
 def rv_size_is_none(size: Variable) -> bool:
-    """Check whether an rv size is None (ie., pt.Constant([]))"""
+    """Check whether the size of a random variable is None.
+
+    Parameters
+    ----------
+    size : Variable
+        The size variable to check.
+
+    Returns
+    -------
+    bool
+        True if the size is None (i.e., pt.Constant([])), False otherwise.
+    """
     return size.type.shape == (0,)  # type: ignore [attr-defined]
 
 
@@ -311,19 +337,21 @@ def change_dist_size(
 
     Parameters
     ----------
-    dist:
+    dist : TensorVariable
         The old distribution to be resized.
-    new_size:
+    new_size : Union[int, Tuple[int, ...], TensorVariable]
         The new size of the distribution.
-    expand: bool, optional
-        If True, `new_size` is prepended to the existing distribution `size`, so that
-        the final size is equal to (*new_size, *dist.size). Defaults to false.
+    expand : bool, optional
+        If True, `new_size` is prepended to the existing distribution `size`,
+        so that the final size is equal to (*new_size, *dist.size).
+        Defaults to False.
 
     Returns
     -------
-    A new distribution variable that is equivalent to the original distribution with
-    the new size. The new distribution will not reuse the old RandomState/Generator
-    input, so it will be independent from the original distribution.
+    TensorVariable
+        A new distribution variable equivalent to the original distribution
+        with the new size. The new distribution will not reuse the old
+        RandomState/Generator input, making it independent from the original.
 
     Examples
     --------