update docs

python/paddle/distribution/binomial.py

@@ -26,7 +26,7 @@ class Binomial(distribution.Distribution):
     r"""
     The Binomial distribution with size `total_count` and `probability` parameters.
 
-    In probability theory and statistics, the binomial distribution is the most basic probability distribution,
+    In probability theory and statistics, the binomial distribution is the most basic discrete probability distribution defined on :math:`[0, n] \cap \mathbb{N}`,
     which can be viewed as the number of times a potentially unfair coin is tossed to get heads, and the result
     of its random variable can be viewed as the sum of a series of independent Bernoulli experiments.
 
@@ -38,15 +38,14 @@ class Binomial(distribution.Distribution):
 
     In the above equation:
 
-    * :math:`total_count = n`: is the size.
-    * :math:`probability = p`: is the probability.
+    * :math:`total_count = n`: is the size, meaning the total number of Bernoulli experiments.
+    * :math:`probability = p`: is the probability of the event happening in one Bernoulli experiments.
 
     Args:
-        total_count(int|Tensor): The size of Binomial distribution, meaning the number of independent bernoulli
-                                trials with probability parameter p. The random variable counts the number of success
-                                among n independent bernoulli trials. The data type of `total_count` will be convert to float32.
-        probability(float|Tensor): The probability of Binomial distribution, meaning the probability of success
-                                for each individual bernoulli trial. The data type of `probability` will be convert to float32.
+        total_count(int|Tensor): The size of Binomial distribution which should be greater than 0, meaning the number of independent bernoulli
+                                trials with probability parameter :math:`p`. The data type of :attr:`total_count` will be convert to float32.
+        probability(float|Tensor): The probability of Binomial distribution which should reside in [0, 1], meaning the probability of success
+                                for each individual bernoulli trial. The data type of :attr:`probability` will be convert to float32.
 
     Examples:
         .. code-block:: python
@@ -141,13 +140,13 @@ def variance(self):
         return self.total_count * self.probability * (1 - self.probability)
 
     def sample(self, shape=()):
-        """Generate binomial samples of the specified shape.
+        """Generate binomial samples of the specified shape. The final shape would be ``shape+batch_shape`` .
 
         Args:
             shape (Sequence[int], optional): Prepended shape of the generated samples.
 
         Returns:
-            Tensor: A tensor with prepended dimensions shape. The data type is float32.
+            Tensor: Sampled data with shape `sample_shape` + `batch_shape`.
         """
         if not isinstance(shape, Iterable):
             raise TypeError('sample shape must be Iterable object.')
@@ -259,7 +258,7 @@ def prob(self, value):
         return paddle.exp(self.log_prob(value))
 
     def kl_divergence(self, other):
-        r"""The KL-divergence between two binomial distributions.
+        r"""The KL-divergence between two binomial distributions with the same :attr:`total_count`.
 
         The probability density function (pdf) is
 

python/paddle/distribution/poisson.py

@@ -26,8 +26,8 @@ class Poisson(distribution.Distribution):
     r"""
     The Poisson distribution with occurrence rate parameter: `rate`.
 
-    In probability theory and statistics, the Poisson distribution is the most basic probability
-    distribution, which is used to describe the probability distribution of the number of random
+    In probability theory and statistics, the Poisson distribution is the most basic discrete probability
+    distribution defined on the nonnegative integer set, which is used to describe the probability distribution of the number of random
     events occurring per unit time.
 
     The probability mass function (pmf) is
@@ -41,7 +41,7 @@ class Poisson(distribution.Distribution):
     * :math:`rate = \lambda`: is the mean occurrence rate.
 
     Args:
-        rate(int|float|Tensor): The mean occurrence rate of Poisson distribution, meaning the expected occurrence
+        rate(int|float|Tensor): The mean occurrence rate of Poisson distribution which should be greater than 0, meaning the expected occurrence
                                 times of an event in a fixed time interval. The data type of `rate` will be convert to float32.
 
     Examples:
@@ -133,13 +133,13 @@ def variance(self):
         return self.rate
 
     def sample(self, shape=()):
-        """Generate poisson samples of the specified shape.
+        """Generate poisson samples of the specified shape. The final shape would be ``shape+batch_shape`` .
 
         Args:
             shape (Sequence[int], optional): Prepended shape of the generated samples.
 
         Returns:
-            Tensor: A tensor with prepended dimensions shape. The data type is float32.
+            Tensor: Sampled data with shape `sample_shape` + `batch_shape`.
         """
         if not isinstance(shape, Iterable):
             raise TypeError('sample shape must be Iterable object.')
@@ -245,7 +245,7 @@ def prob(self, value):
         return paddle.exp(self.log_prob(value))
 
     def kl_divergence(self, other):
-        r"""The KL-divergence between two poisson distributions.
+        r"""The KL-divergence between two poisson distributions with the same `batch_shape`.
 
         The probability density function (pdf) is