Type Gamma
Namespace tensorflow.distributions
Parent Distribution
Interfaces IGamma
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 the paper [Michael Figurnov, Shakir Mohamed, Andriy Mnih.
Implicit Reparameterization Gradients, 2018](https://arxiv.org/abs/1805.08498) #### Examples
Compute the gradients of samples w.r.t. the parameters:
Show Example
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])
Properties
Public properties
object allow_nan_stats get;
object allow_nan_stats_dyn get;
TensorShape batch_shape get;
object batch_shape_dyn get;
object concentration get;
Concentration parameter.
object concentration_dyn get;
Concentration parameter.
object dtype get;
object dtype_dyn get;
TensorShape event_shape get;
object event_shape_dyn get;
string name get;
object name_dyn get;
IDictionary<object, object> parameters get;
object parameters_dyn get;
object PythonObject get;
object rate get;
Rate parameter.
object rate_dyn get;
Rate parameter.