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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 | |
__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, alpha, validate_args=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, _instance=None): | |
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) | |
def mean(self): | |
# mean is inf for alpha <= 1 | |
a = self.alpha.clamp(min=1) | |
return a * self.scale / (a - 1) | |
def mode(self): | |
return self.scale | |
def variance(self): | |
# var is inf for alpha <= 2 | |
a = self.alpha.clamp(min=2) | |
return self.scale.pow(2) * a / ((a - 1).pow(2) * (a - 2)) | |
def support(self): | |
return constraints.greater_than_eq(self.scale) | |
def entropy(self): | |
return (self.scale / self.alpha).log() + (1 + self.alpha.reciprocal()) | |