class_docstr: BetaQuotient distribution.
  
  The Beta Quotient distribution is defined over the positive reals, as
  the ratio of two Independent Beta distributed random variables.
  
  In other words:
  
  ```none
  X ~ Beta(a0, b0)
  Y ~ Beta(a1, b1)
  X / Y ~ BetaQuotient(a0, b0, a1, b1)
  ```
  
  The distribution is defined over the positive reals, by four parameters
  `concentration0_numerator`, `concentration1_numerator`,
  `concentration0_denominator` and `concentration1_denominator`
  (aka `beta` and `alpha` of the numerator and denominator Beta distribution
  respectively).
  
  Distribution parameters are automatically broadcast in all functions; see
  examples for details.
  
  Warning: The samples can be zero or inf due to finite precision.
  This happens more often when some of the concentrations are very small.
  
  Samples of this distribution are reparameterized (pathwise differentiable).
  The derivatives are computed using the approach described in [3].
  
  #### Examples
  
  ```python
  import tensorflow_probability as tfp
  tfd = tfp.distributions
  
  # Create a batch of three BetaQuotient distributions.
  alpha0 = [1, 2, 3]
  alpha1 = [5]
  beta0 = [1, 2, 3]
  beta1 = [0.4]
  dist = tfd.BetaQuotient(alpha0, beta0, alpha1, beta1)
  
  dist.sample([4, 5])  # Shape [4, 5, 3]
  
  # `x` has three batch entries, each with two samples.
  x = [[.1, .4, .5],
       [.2, .3, .5]]
  # Calculate the probability of each pair of samples under the corresponding
  # distribution in `dist`.
  dist.prob(x)         # Shape [2, 3]
  ```
  
  #### References
  [1] T. Pham-Gia, Distributions of the ratios of independent beta variables
      and applications. Communications in Statistics, Theory and Methods.
      Volume 29.
  
  [2] S. Nadarajah, Sums, products and ratios of generalized beta variables.
      Statistical Papers, 47.
  
  [3] Michael Figurnov, Shakir Mohamed, Andriy Mnih. Implicit
      Reparameterization Gradients. https://arxiv.org/abs/1805.08498
docstr: Concentration parameter associated with a `1` outcome.
docstr_tok: ["Concentration","parameter","associated","with","a","`","1","`","outcome","."]
code: def concentration1_denominator(self):
      """Concentration parameter associated with a `1` outcome."""
      return self._concentration1_denominator
  
imports: import numpy
  import tensorflow.compat.v2
  from tensorflow_probability.python.bijectors import exp
  from tensorflow_probability.python.bijectors import softplus
  from tensorflow_probability.python.distributions import beta
  from tensorflow_probability.python.distributions import distribution
  from tensorflow_probability.python.internal import assert_util
  from tensorflow_probability.python.internal import distribution_util
  from tensorflow_probability.python.internal import dtype_util
  from tensorflow_probability.python.internal import parameter_properties
  from tensorflow_probability.python.internal import reparameterization
  from tensorflow_probability.python.internal import samplers
  from tensorflow_probability.python.internal import tensor_util
  from tensorflow_probability.python.math import hypergeometric
  from tensorflow_probability.python.math import special
label_desc: Use image node_id 5 for calling the BetaQuotient obj's underlying member method code with example usage: obj.concentration1_denominator() and returns: self