code: import torch
  from torch.distributions import constraints
  from torch.distributions.uniform import Uniform
  from torch.distributions.transformed_distribution import TransformedDistribution
  from torch.distributions.transforms import AffineTransform, PowerTransform
  from torch.distributions.utils import broadcast_all, euler_constant
  
  
  def _moments(a, b, n):
      """
      Computes nth moment of Kumaraswamy using using torch.lgamma
      """
      arg1 = 1 + n / a
      log_value = torch.lgamma(arg1) + torch.lgamma(b) - torch.lgamma(arg1 + b)
      return b * torch.exp(log_value)
  
  
  class Kumaraswamy(TransformedDistribution):
      r"""
      Samples from a Kumaraswamy distribution.
  
      Example::
  
          >>> m = Kumaraswamy(torch.Tensor([1.0]), torch.Tensor([1.0]))
          >>> m.sample()  # sample from a Kumaraswamy distribution with concentration alpha=1 and beta=1
          tensor([ 0.1729])
  
      Args:
          concentration1 (float or Tensor): 1st concentration parameter of the distribution
              (often referred to as alpha)
          concentration0 (float or Tensor): 2nd concentration parameter of the distribution
              (often referred to as beta)
      """
      arg_constraints = {'concentration1': constraints.positive, 'concentration0': constraints.positive}
      support = constraints.unit_interval
      has_rsample = True
  
      def __init__(self, concentration1, concentration0, validate_args=None):
          self.concentration1, self.concentration0 = broadcast_all(concentration1, concentration0)
          finfo = torch.finfo(self.concentration0.dtype)
          base_dist = Uniform(torch.full_like(self.concentration0, 0),
                              torch.full_like(self.concentration0, 1))
          transforms = [PowerTransform(exponent=self.concentration0.reciprocal()),
                        AffineTransform(loc=1., scale=-1.),
                        PowerTransform(exponent=self.concentration1.reciprocal())]
          super(Kumaraswamy, self).__init__(base_dist, transforms, validate_args=validate_args)
  
      def expand(self, batch_shape, _instance=None):
          new = self._get_checked_instance(Kumaraswamy, _instance)
          new.concentration1 = self.concentration1.expand(batch_shape)
          new.concentration0 = self.concentration0.expand(batch_shape)
          return super(Kumaraswamy, self).expand(batch_shape, _instance=new)
  
      @property
      def mean(self):
          return _moments(self.concentration1, self.concentration0, 1)
  
      @property
      def variance(self):
          return _moments(self.concentration1, self.concentration0, 2) - torch.pow(self.mean, 2)
  
      def entropy(self):
          t1 = (1 - self.concentration1.reciprocal())
          t0 = (1 - self.concentration0.reciprocal())
          H0 = torch.digamma(self.concentration0 + 1) + euler_constant
          return t0 + t1 * H0 - torch.log(self.concentration1) - torch.log(self.concentration0)
  