class_docstr: Gamma distribution.
  
  The Gamma distribution is defined over positive real numbers using
  parameters `concentration` (aka "alpha") and `rate` (aka "beta").
  
  #### Mathematical Details
  
  The probability density function (pdf) is,
  
  ```none
  pdf(x; alpha, beta, x > 0) = x**(alpha - 1) exp(-x beta) / Z
  Z = Gamma(alpha) beta**(-alpha)
  ```
  
  where:
  
  * `concentration = alpha`, `alpha > 0`,
  * `rate = beta`, `beta > 0`,
  * `Z` is the normalizing constant, and,
  * `Gamma` is the [gamma function](
    https://en.wikipedia.org/wiki/Gamma_function).
  
  The cumulative density function (cdf) is,
  
  ```none
  cdf(x; alpha, beta, x > 0) = GammaInc(alpha, beta x) / Gamma(alpha)
  ```
  
  where `GammaInc` is the [lower incomplete Gamma function](
  https://en.wikipedia.org/wiki/Incomplete_gamma_function).
  
  The parameters can be intuited via their relationship to mean and stddev,
  
  ```none
  concentration = alpha = (mean / stddev)**2
  rate = beta = mean / stddev**2 = concentration / mean
  ```
  
  Distribution parameters are automatically broadcast in all functions; see
  examples for details.
  
  Warning: The samples of this distribution are always non-negative. However,
  the samples that are smaller than `np.finfo(dtype).tiny` are rounded
  to this value, so it appears more often than it should.
  This should only be noticeable when the `concentration` is very small, or the
  `rate` is very large. See note in `tf.random.gamma` docstring.
  
  Samples of this distribution are reparameterized (pathwise differentiable).
  The derivatives are computed using the approach described in
  (Figurnov et al., 2018).
  
  #### Examples
  
  ```python
  import tensorflow_probability as tfp
  tfd = tfp.distributions
  
  dist = tfd.Gamma(concentration=3.0, rate=2.0)
  dist2 = tfd.Gamma(concentration=[3.0, 4.0], rate=[2.0, 3.0])
  ```
  
  Compute the gradients of samples w.r.t. the parameters:
  
  ```python
  concentration = tf.constant(3.0)
  rate = tf.constant(2.0)
  dist = tfd.Gamma(concentration, rate)
  samples = dist.sample(5)  # Shape [5]
  loss = tf.reduce_mean(tf.square(samples))  # Arbitrary loss function
  # Unbiased stochastic gradients of the loss function
  grads = tf.gradients(loss, [concentration, rate])
  ```
  
  References:
    Implicit Reparameterization Gradients:
      [Figurnov et al., 2018]
      (http://papers.nips.cc/paper/7326-implicit-reparameterization-gradients)
      ([pdf](http://papers.nips.cc/paper/7326-implicit-reparameterization-gradients.pdf))
docstr: Construct Gamma with `concentration` and `rate` parameters.
  
  The parameters `concentration` and `rate` must be shaped in a way that
  supports broadcasting (e.g. `concentration + rate` is a valid operation).
  
  Args:
    concentration: Floating point tensor, the concentration params of the
      distribution(s). Must contain only positive values.
    rate: Floating point tensor, the inverse scale params of the
      distribution(s). Must contain only positive values.
    validate_args: Python `bool`, default `False`. When `True` distribution
      parameters are checked for validity despite possibly degrading runtime
      performance. When `False` invalid inputs may silently render incorrect
      outputs.
    allow_nan_stats: Python `bool`, default `True`. When `True`, statistics
      (e.g., mean, mode, variance) use the value "`NaN`" to indicate the
      result is undefined. When `False`, an exception is raised if one or
      more of the statistic's batch members are undefined.
    name: Python `str` name prefixed to Ops created by this class.
  
  Raises:
    TypeError: if `concentration` and `rate` are different dtypes.
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code: def __init__(
      self,
      concentration,
      rate,
      validate_args=False,
      allow_nan_stats=True,
      name="Gamma",
  ):
      """Construct Gamma with `concentration` and `rate` parameters.
  
      The parameters `concentration` and `rate` must be shaped in a way that
      supports broadcasting (e.g. `concentration + rate` is a valid operation).
  
      Args:
        concentration: Floating point tensor, the concentration params of the
          distribution(s). Must contain only positive values.
        rate: Floating point tensor, the inverse scale params of the
          distribution(s). Must contain only positive values.
        validate_args: Python `bool`, default `False`. When `True` distribution
          parameters are checked for validity despite possibly degrading runtime
          performance. When `False` invalid inputs may silently render incorrect
          outputs.
        allow_nan_stats: Python `bool`, default `True`. When `True`, statistics
          (e.g., mean, mode, variance) use the value "`NaN`" to indicate the
          result is undefined. When `False`, an exception is raised if one or
          more of the statistic's batch members are undefined.
        name: Python `str` name prefixed to Ops created by this class.
  
      Raises:
        TypeError: if `concentration` and `rate` are different dtypes.
      """
      parameters = dict(locals())
      with ops.name_scope(name, values=[concentration, rate]) as name:
          with ops.control_dependencies(
              [
                  check_ops.assert_positive(concentration),
                  check_ops.assert_positive(rate),
              ]
              if validate_args
              else []
          ):
              self._concentration = array_ops.identity(
                  concentration, name="concentration"
              )
              self._rate = array_ops.identity(rate, name="rate")
              check_ops.assert_same_float_dtype(
                  [self._concentration, self._rate]
              )
      super(Gamma, self).__init__(
          dtype=self._concentration.dtype,
          validate_args=validate_args,
          allow_nan_stats=allow_nan_stats,
          reparameterization_type=distribution.FULLY_REPARAMETERIZED,
          parameters=parameters,
          graph_parents=[self._concentration, self._rate],
          name=name,
      )
  
imports: import numpy
  from tensorflow.python.framework import constant_op
  from tensorflow.python.framework import dtypes
  from tensorflow.python.framework import ops
  from tensorflow.python.framework import tensor_shape
  from tensorflow.python.ops import array_ops
  from tensorflow.python.ops import check_ops
  from tensorflow.python.ops import control_flow_ops
  from tensorflow.python.ops import math_ops
  from tensorflow.python.ops import nn
  from tensorflow.python.ops import random_ops
  from tensorflow.python.ops.distributions import distribution
  from tensorflow.python.ops.distributions import kullback_leibler
  from tensorflow.python.ops.distributions import util
  from tensorflow.python.util import deprecation
  from tensorflow.python.util.tf_export import tf_export
label_desc: Use image node_id 1 to create a new Gamma object from inherited base classes: distribution with example: obj = Gamma(concentration, rate, validate_args, allow_nan_stats, name)