pytorch

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import torch
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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.gumbel import euler_constant
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from torch.distributions.transformed_distribution import TransformedDistribution
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from torch.distributions.transforms import AffineTransform, PowerTransform
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from torch.distributions.utils import broadcast_all
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__all__ = ["Weibull"]
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class Weibull(TransformedDistribution):
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    r"""
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    Samples from a two-parameter Weibull distribution.
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    Example:
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        >>> # xdoctest: +IGNORE_WANT("non-deterministic")
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        >>> m = Weibull(torch.tensor([1.0]), torch.tensor([1.0]))
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        >>> m.sample()  # sample from a Weibull distribution with scale=1, concentration=1
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        tensor([ 0.4784])
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    Args:
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        scale (float or Tensor): Scale parameter of distribution (lambda).
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        concentration (float or Tensor): Concentration parameter of distribution (k/shape).
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    """
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    arg_constraints = {
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        "scale": constraints.positive,
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        "concentration": constraints.positive,
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    }
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    support = constraints.positive
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    def __init__(self, scale, concentration, validate_args=None):
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        self.scale, self.concentration = broadcast_all(scale, concentration)
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        self.concentration_reciprocal = self.concentration.reciprocal()
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        base_dist = Exponential(
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            torch.ones_like(self.scale), validate_args=validate_args
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        )
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        transforms = [
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            PowerTransform(exponent=self.concentration_reciprocal),
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            AffineTransform(loc=0, scale=self.scale),
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        ]
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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(Weibull, _instance)
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        new.scale = self.scale.expand(batch_shape)
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        new.concentration = self.concentration.expand(batch_shape)
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        new.concentration_reciprocal = new.concentration.reciprocal()
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        base_dist = self.base_dist.expand(batch_shape)
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        transforms = [
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            PowerTransform(exponent=new.concentration_reciprocal),
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            AffineTransform(loc=0, scale=new.scale),
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        ]
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        super(Weibull, new).__init__(base_dist, transforms, validate_args=False)
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        new._validate_args = self._validate_args
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        return new
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    @property
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    def mean(self):
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        return self.scale * torch.exp(torch.lgamma(1 + self.concentration_reciprocal))
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    @property
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    def mode(self):
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        return (
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            self.scale
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            * ((self.concentration - 1) / self.concentration)
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            ** self.concentration.reciprocal()
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        )
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    @property
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    def variance(self):
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        return self.scale.pow(2) * (
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            torch.exp(torch.lgamma(1 + 2 * self.concentration_reciprocal))
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            - torch.exp(2 * torch.lgamma(1 + self.concentration_reciprocal))
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        )
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    def entropy(self):
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        return (
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            euler_constant * (1 - self.concentration_reciprocal)
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            + torch.log(self.scale * self.concentration_reciprocal)
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            + 1
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        )
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