# 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) 

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]) 

### Public properties

#### objectconcentration get;

Concentration parameter.

#### objectconcentration_dyn get;

Concentration parameter.

Rate parameter.

Rate parameter.