tf.compat.v1.distributions.Gamma

Gamma distribution.

Inherits From: 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,

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.

The cumulative density function (cdf) is,

cdf(x; alpha, beta, x > 0) = GammaInc(alpha, beta x) / Gamma(alpha)

where GammaInc is the