refine Categorical and MultivariateNormalDiag en doc (#20723)

* refine Categorical and MultivariateNormalDiag en doc test=develop, test=document_fix

* refine Categorical and MultivariateNormalDiag en doc test=develop, test=document_fix

python/paddle/fluid/layers/distributions.py

@@ -404,8 +404,18 @@ class Categorical(Distribution):
     one of K possible categories, with the probability of each category 
     separately specified.
 
+    The probability mass function (pmf) is:
+
+    .. math::
+
+        pmf(k; p_i) = \prod_{i=1}^{k} p_i^{[x=i]}
+
+    In the above equation:
+
+    * :math:`[x=i]` : it evaluates to 1 if :math:`x==i` , 0 otherwise.
+
     Args:
-        logits(list|numpy.ndarray|Variable): The logits input of categorical distribution.
+        logits(list|numpy.ndarray|Variable): The logits input of categorical distribution. The data type is float32.
 
     Examples:
         .. code-block:: python
@@ -439,7 +449,7 @@ class Categorical(Distribution):
     def __init__(self, logits):
         """
         Args:
-            logits: A float32 tensor
+            logits(list|numpy.ndarray|Variable): The logits input of categorical distribution. The data type is float32.
         """
         if self._validate_args(logits):
             self.logits = logits
@@ -450,7 +460,7 @@ class Categorical(Distribution):
         """The KL-divergence between two Categorical distributions.
 
         Args:
-            other (Categorical): instance of Categorical.
+            other (Categorical): instance of Categorical. The data type is float32.
 
         Returns:
             Variable: kl-divergence between two Categorical distributions.
@@ -477,7 +487,7 @@ class Categorical(Distribution):
         """Shannon entropy in nats.
 
         Returns:
-          Variable: Shannon entropy of Categorical distribution.
+          Variable: Shannon entropy of Categorical distribution. The data type is float32.
 
         """
         logits = self.logits - nn.reduce_max(self.logits, dim=-1, keep_dim=True)
@@ -495,10 +505,31 @@ class MultivariateNormalDiag(Distribution):
     A multivariate normal (also called Gaussian) distribution parameterized by a mean vector
     and a covariance matrix.
 
+    The probability density function (pdf) is:
+
+    .. math::
+
+        pdf(x; loc, scale) = \\frac{e^{-\\frac{||y||^2}{2}}}{Z}
+
+    where:
+    .. math::
+
+        y = inv(scale) @ (x - loc)
+        Z = (2\\pi)^{0.5k} |det(scale)|
+
+
+    In the above equation:
+
+    * :math:`inv` : denotes to take the inverse of the matrix.
+    * :math:`@` : denotes matrix multiplication.
+    * :math:`det` : denotes to evaluate the determinant.
+
     Args:
-        loc(list|numpy.ndarray|Variable): The mean of multivariateNormal distribution.
+        loc(list|numpy.ndarray|Variable): The mean of multivariateNormal distribution with shape :math:`[k]` .
-        scale(list|numpy.ndarray|Variable): The positive definite diagonal covariance matrix of
+            The data type is float32.
-        multivariateNormal distribution.
+        scale(list|numpy.ndarray|Variable): The positive definite diagonal covariance matrix of multivariateNormal
+            distribution  with shape :math:`[k, k]` . All elements are 0 except diagonal elements. The data type is
+            float32.
 
     Examples:
         .. code-block:: python
@@ -570,7 +601,7 @@ class MultivariateNormalDiag(Distribution):
         """Shannon entropy in nats.
 
         Returns:
-          Variable: Shannon entropy of Multivariate Normal distribution.
+          Variable: Shannon entropy of Multivariate Normal distribution. The data type is float32.
 
         """
         entropy = 0.5 * (
@@ -586,7 +617,7 @@ class MultivariateNormalDiag(Distribution):
             other (MultivariateNormalDiag): instance of Multivariate Normal.
 
         Returns:
-            Variable: kl-divergence between two Multivariate Normal distributions.
+            Variable: kl-divergence between two Multivariate Normal distributions. The data type is float32.
 
         """
         assert isinstance(other, MultivariateNormalDiag)