xref: /aosp_15_r20/external/pytorch/torch/distributions/pareto.py (revision da0073e96a02ea20f0ac840b70461e3646d07c45) 
1# mypy: allow-untyped-defs
2from torch.distributions import constraints
3from torch.distributions.exponential import Exponential
4from torch.distributions.transformed_distribution import TransformedDistribution
5from torch.distributions.transforms import AffineTransform, ExpTransform
6from torch.distributions.utils import broadcast_all
7
8
9__all__ = ["Pareto"]
10
11
12class Pareto(TransformedDistribution):
13    r"""
14    Samples from a Pareto Type 1 distribution.
15
16    Example::
17
18        >>> # xdoctest: +IGNORE_WANT("non-deterministic")
19        >>> m = Pareto(torch.tensor([1.0]), torch.tensor([1.0]))
20        >>> m.sample()  # sample from a Pareto distribution with scale=1 and alpha=1
21        tensor([ 1.5623])
22
23    Args:
24        scale (float or Tensor): Scale parameter of the distribution
25        alpha (float or Tensor): Shape parameter of the distribution
26    """
27    arg_constraints = {"alpha": constraints.positive, "scale": constraints.positive}
28
29    def __init__(self, scale, alpha, validate_args=None):
30        self.scale, self.alpha = broadcast_all(scale, alpha)
31        base_dist = Exponential(self.alpha, validate_args=validate_args)
32        transforms = [ExpTransform(), AffineTransform(loc=0, scale=self.scale)]
33        super().__init__(base_dist, transforms, validate_args=validate_args)
34
35    def expand(self, batch_shape, _instance=None):
36        new = self._get_checked_instance(Pareto, _instance)
37        new.scale = self.scale.expand(batch_shape)
38        new.alpha = self.alpha.expand(batch_shape)
39        return super().expand(batch_shape, _instance=new)
40
41    @property
42    def mean(self):
43        # mean is inf for alpha <= 1
44        a = self.alpha.clamp(min=1)
45        return a * self.scale / (a - 1)
46
47    @property
48    def mode(self):
49        return self.scale
50
51    @property
52    def variance(self):
53        # var is inf for alpha <= 2
54        a = self.alpha.clamp(min=2)
55        return self.scale.pow(2) * a / ((a - 1).pow(2) * (a - 2))
56
57    @constraints.dependent_property(is_discrete=False, event_dim=0)
58    def support(self):
59        return constraints.greater_than_eq(self.scale)
60
61    def entropy(self):
62        return (self.scale / self.alpha).log() + (1 + self.alpha.reciprocal())
63