class_docstr: Log-logistic distribution.
  
  A very heavy-tailed distribution over positive real numbers.
  https://en.wikipedia.org/wiki/Log-logistic_distribution
  
  Drawing :math:`x \sim \operatorname{Loglogistic}(\mu, \sigma)` is
  equivalent to:
  
  .. math::
  
      y &\sim \operatorname{Logistic}(\mu, \sigma)\\
      x &= \exp(y)
docstr: Logarithm of the intensity (a.k.a. hazard) function.
  
  The intensity is defined as :math:`\lambda(x) = p(x) / S(x)`.
  
  We define :math:`z = (\log(x) - \mu) / \sigma` and obtain the intensity
  as :math:`\lambda(x) = sigmoid(z) / (\sigma * \log(x))`, or
  equivalently
  :math:`\log \lambda(x) = z - \log(1 + \exp(z)) - \log(\sigma) - \log(x)`.
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code: def log_intensity(self, x: Tensor) -> Tensor:
      r"""
      Logarithm of the intensity (a.k.a. hazard) function.
  
      The intensity is defined as :math:`\lambda(x) = p(x) / S(x)`.
  
      We define :math:`z = (\log(x) - \mu) / \sigma` and obtain the intensity
      as :math:`\lambda(x) = sigmoid(z) / (\sigma * \log(x))`, or
      equivalently
      :math:`\log \lambda(x) = z - \log(1 + \exp(z)) - \log(\sigma) - \log(x)`.
      """  # noqa: E501
  
      log_x = x.clip(1e-20, np.inf).log()
      z = (log_x - self.mu) / self.sigma
      F = getF(x)
      return z - self.sigma.log() - F.Activation(z, "softrelu") - log_x
  
imports: from typing import Dict, Optional, Tuple
  import numpy
  from mxnet import autograd, nd
  from gluonts.core.component import validated
  from gluonts.mx import Tensor
  from gluonts.mx.distribution.distribution import getF
  from .base import TPPDistribution, TPPDistributionOutput
label_desc: Use image node_id 6 for calling the Loglogistic obj's underlying member method code with example usage: obj.log_intensity(x) and returns: unknown