Poisson¶
- class paddle.distribution. Poisson ( rate ) [source]
-
The Poisson distribution with occurrence rate parameter: rate.
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
\[pmf(x; \lambda) = \frac{e^{-\lambda} \cdot \lambda^x}{x!}\]In the above equation:
\(rate = \lambda\): is the mean occurrence rate.
- Parameters
-
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. If the input data type is int or float, the data type of rate will be converted to a 1-D Tensor with paddle global default dtype.
Examples
>>> import paddle >>> from paddle.distribution import Poisson >>> paddle.set_device('cpu') >>> paddle.seed(100) >>> rv = Poisson(paddle.to_tensor(30.0)) >>> print(rv.sample([3])) Tensor(shape=[3, 1], dtype=float32, place=Place(cpu), stop_gradient=True, [[35.], [35.], [30.]]) >>> print(rv.mean) Tensor(shape=[], dtype=float32, place=Place(cpu), stop_gradient=True, 30.) >>> print(rv.entropy()) Tensor(shape=[1], dtype=float32, place=Place(cpu), stop_gradient=True, [3.11671066]) >>> rv1 = Poisson(paddle.to_tensor([[30.,40.],[8.,5.]])) >>> rv2 = Poisson(paddle.to_tensor([[1000.,40.],[7.,10.]])) >>> print(rv1.kl_divergence(rv2)) Tensor(shape=[2, 2], dtype=float32, place=Place(cpu), stop_gradient=True, [[864.80285645, 0. ], [0.06825157 , 1.53426421 ]])
- property mean
-
Mean of poisson distribution.
- Returns
-
mean value.
- Return type
-
Tensor
- property variance
-
Variance of poisson distribution.
- Returns
-
variance value.
- Return type
-
Tensor
-
sample
(
shape=()
)
sample¶
-
Generate poisson samples of the specified shape. The final shape would be
shape+batch_shape.- Parameters
-
shape (Sequence[int], optional) – Prepended shape of the generated samples.
- Returns
-
Sampled data with shape sample_shape + batch_shape.
- Return type
-
Tensor
-
entropy
(
)
entropy¶
-
Shannon entropy in nats.
The entropy is
\[\mathcal{H}(X) = - \sum_{x \in \Omega} p(x) \log{p(x)}\]In the above equation:
\(\Omega\): is the support of the distribution.
- Returns
-
Shannon entropy of poisson distribution. The data type is the same as rate.
- Return type
-
Tensor
-
log_prob
(
value
)
log_prob¶
-
Log probability density/mass function.
- Parameters
-
value (Tensor) – The input tensor.
- Returns
-
log probability. The data type is the same as rate.
- Return type
-
Tensor
-
prob
(
value
)
prob¶
-
Probability density/mass function.
- Parameters
-
value (Tensor) – The input tensor.
- Returns
-
probability. The data type is the same as rate.
- Return type
-
Tensor
-
kl_divergence
(
other
)
[source]
kl_divergence¶
-
The KL-divergence between two poisson distributions with the same batch_shape.
The probability density function (pdf) is
\[KL\_divergence\lambda_1, \lambda_2) = \sum_x p_1(x) \log{\frac{p_1(x)}{p_2(x)}}\]\[p_1(x) = \frac{e^{-\lambda_1} \cdot \lambda_1^x}{x!}\]\[p_2(x) = \frac{e^{-\lambda_2} \cdot \lambda_2^x}{x!}\]- Parameters
-
other (Poisson) – instance of
Poisson. - Returns
-
Tensor, kl-divergence between two poisson distributions. The data type is the same as rate.
- property batch_shape
-
Returns batch shape of distribution
- Returns
-
batch shape
- Return type
-
Sequence[int]
- property event_shape
-
Returns event shape of distribution
- Returns
-
event shape
- Return type
-
Sequence[int]
-
probs
(
value
)
probs¶
-
Probability density/mass function.
Note
This method will be deprecated in the future, please use prob instead.
-
rsample
(
shape=()
)
rsample¶
-
reparameterized sample