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