# Source code for tensorplay.distributions.poisson

Source: https://www.tensorplay.cn/docs/_modules/tensorplay/distributions/poisson.html

```
# mypy: allow-untyped-defs

import tensorplay
from tensorplay import Tensor
from tensorplay.distributions import constraints
from tensorplay.distributions.exp_family import ExponentialFamily
from tensorplay.distributions.utils import broadcast_all
from tensorplay.distributions._types import _Number, Number

__all__ = ["Poisson"]

[docs]
class Poisson(ExponentialFamily):
    r"""
    Creates a Poisson distribution parameterized by :attr:`rate`, the rate parameter.

    Samples are nonnegative integers, with a pmf given by

    .. math::
      \mathrm{rate}^k \frac{e^{-\mathrm{rate}}}{k!}

    Example::

        >>> # xdoctest: +SKIP("poisson_cpu not implemented for 'Long'")
        >>> m = Poisson(tensorplay.tensor([4]))
        >>> m.sample()
        tensor([ 3.])

    Args:
        rate (Number, Tensor): the rate parameter
    """

    # pyrefly: ignore [bad-override]
    arg_constraints = {"rate": constraints.nonnegative}
    support = constraints.nonnegative_integer

    @property
    def mean(self) -> Tensor:
        return self.rate

    @property
    def mode(self) -> Tensor:
        return self.rate.floor()

    @property
    def variance(self) -> Tensor:
        return self.rate

    def __init__(
        self,
        rate: Tensor | Number,
        validate_args: bool | None = None,
    ) -> None:
        (self.rate,) = broadcast_all(rate)
        if isinstance(rate, _Number):
            batch_shape = tensorplay.Size()
        else:
            batch_shape = self.rate.size()
        super().__init__(batch_shape, validate_args=validate_args)

    def expand(self, batch_shape, _instance=None):
        new = self._get_checked_instance(Poisson, _instance)
        batch_shape = tensorplay.Size(batch_shape)
        new.rate = self.rate.expand(batch_shape)
        super(Poisson, new).__init__(batch_shape, validate_args=False)
        new._validate_args = self._validate_args
        return new

    def sample(self, sample_shape=tensorplay.Size()):
        shape = self._extended_shape(sample_shape)
        with tensorplay.no_grad():
            return tensorplay.poisson(self.rate.expand(shape))

    def log_prob(self, value):
        if self._validate_args:
            self._validate_sample(value)
        rate, value = broadcast_all(self.rate, value)
        return value.xlogy(rate) - rate - (value + 1).lgamma()

    @property
    def _natural_params(self) -> tuple[Tensor]:
        return (tensorplay.log(self.rate),)

    # pyrefly: ignore [bad-override]
    def _log_normalizer(self, x):
        return tensorplay.exp(x)
```