pytorch

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