# mypy: allow-untyped-defs
import torch
from torch import Tensor
from torch.distributions import constraints
from torch.distributions.exp_family import ExponentialFamily
from torch.distributions.utils import broadcast_all
from torch.types import _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(torch.tensor([4]))
>>> m.sample()
tensor([ 3.])
Args:
rate (Number, Tensor): the rate parameter
"""
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, validate_args=None):
(self.rate,) = broadcast_all(rate)
if isinstance(rate, _Number):
batch_shape = torch.Size()
else:
batch_shape = self.rate.size()
super().__init__(batch_shape, validate_args=validate_args)
[docs] def expand(self, batch_shape, _instance=None):
new = self._get_checked_instance(Poisson, _instance)
batch_shape = torch.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
[docs] def sample(self, sample_shape=torch.Size()):
shape = self._extended_shape(sample_shape)
with torch.no_grad():
return torch.poisson(self.rate.expand(shape))
[docs] 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 (torch.log(self.rate),)
def _log_normalizer(self, x):
return torch.exp(x)
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