LostTech.TensorFlow : API Documentation

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) ```


* `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])


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.

object reparameterization_type get;

object reparameterization_type_dyn get;

object validate_args get;

object validate_args_dyn get;