Poisson¶

class paddle.distribution. Poisson ( rate: float | Tensor ) [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], dtype=float32, place=Place(cpu), stop_gradient=True,
[32., 27., 25.])

>>> print(rv.mean)
Tensor(shape=[], dtype=float32, place=Place(cpu), stop_gradient=True,
30.)

>>> print(rv.entropy())
Tensor(shape=[], dtype=float32, place=Place(cpu), stop_gradient=True,
3.11671519)

>>> 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,
[[864.80499268, 0.          ],
 [0.06825146  , 1.53426409  ]])

property mean : Tensor

Mean of poisson distribution.

Returns: mean value.
Return type: Tensor

property variance : Tensor

Variance of poisson distribution.

Returns: variance value.
Return type: Tensor

sample ( shape: Sequence[int] = [] ) → Tensor 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 ( ) → Tensor 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: Tensor ) → Tensor 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

property batch_shape : Sequence[int]

Returns batch shape of distribution

Returns: batch shape
Return type: Sequence[int]

property event_shape : Sequence[int]

Returns event shape of distribution

Returns: event shape
Return type: Sequence[int]

prob ( value: Tensor ) → Tensor prob¶

Probability density/mass function.

Parameters: value (Tensor) – The input tensor.
Returns: probability. The data type is the same as rate.
Return type: Tensor

probs ( value: Tensor ) → Tensor probs¶: Probability density/mass function.

Note

This method will be deprecated in the future, please use prob instead.

rsample ( shape: Sequence[int] = [] ) → Tensor rsample¶: reparameterized sample

kl_divergence ( other: Poisson ) → Tensor [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.

Poisson¶

sample¶

entropy¶

log_prob¶

prob¶

probs¶

rsample¶

kl_divergence¶