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- from typing import Optional, Union
- from torch import Tensor
- from torch.distributions import constraints
- from torch.distributions.exponential import Exponential
- from torch.distributions.transformed_distribution import TransformedDistribution
- from torch.distributions.transforms import AffineTransform, ExpTransform
- from torch.distributions.utils import broadcast_all
- from torch.types import _size
- __all__ = ["Pareto"]
- class Pareto(TransformedDistribution):
- r"""
- Samples from a Pareto Type 1 distribution.
- Example::
- >>> # xdoctest: +IGNORE_WANT("non-deterministic")
- >>> m = Pareto(torch.tensor([1.0]), torch.tensor([1.0]))
- >>> m.sample() # sample from a Pareto distribution with scale=1 and alpha=1
- tensor([ 1.5623])
- Args:
- scale (float or Tensor): Scale parameter of the distribution
- alpha (float or Tensor): Shape parameter of the distribution
- """
- arg_constraints = {"alpha": constraints.positive, "scale": constraints.positive}
- def __init__(
- self,
- scale: Union[Tensor, float],
- alpha: Union[Tensor, float],
- validate_args: Optional[bool] = None,
- ) -> None:
- self.scale, self.alpha = broadcast_all(scale, alpha)
- base_dist = Exponential(self.alpha, validate_args=validate_args)
- transforms = [ExpTransform(), AffineTransform(loc=0, scale=self.scale)]
- super().__init__(base_dist, transforms, validate_args=validate_args)
- def expand(
- self, batch_shape: _size, _instance: Optional["Pareto"] = None
- ) -> "Pareto":
- new = self._get_checked_instance(Pareto, _instance)
- new.scale = self.scale.expand(batch_shape)
- new.alpha = self.alpha.expand(batch_shape)
- return super().expand(batch_shape, _instance=new)
- @property
- def mean(self) -> Tensor:
- # mean is inf for alpha <= 1
- a = self.alpha.clamp(min=1)
- return a * self.scale / (a - 1)
- @property
- def mode(self) -> Tensor:
- return self.scale
- @property
- def variance(self) -> Tensor:
- # var is inf for alpha <= 2
- a = self.alpha.clamp(min=2)
- return self.scale.pow(2) * a / ((a - 1).pow(2) * (a - 2))
- @constraints.dependent_property(is_discrete=False, event_dim=0)
- def support(self) -> constraints.Constraint:
- return constraints.greater_than_eq(self.scale)
- def entropy(self) -> Tensor:
- return (self.scale / self.alpha).log() + (1 + self.alpha.reciprocal())
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