Source code for torch.distributions.pareto

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

[docs]class Pareto(TransformedDistribution): r""" Samples from a Pareto Type 1 distribution. Example:: >>> 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(Pareto, self).__init__(base_dist, transforms, validate_args=validate_args)
[docs] 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(Pareto, self).expand(batch_shape, _instance=new)
@property def mean(self): # mean is inf for alpha <= 1 a = self.alpha.clamp(min=1) return a * self.scale / (a - 1) @property 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)) @constraints.dependent_property(is_discrete=False, event_dim=0) def support(self): return constraints.greater_than(self.scale)
[docs] def entropy(self): return ((self.scale / self.alpha).log() + (1 + self.alpha.reciprocal()))


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