Gamma StructureInfer.NET Documentation
Microsoft Research, Cambridge
A Gamma distribution on positive reals.

Namespace: MicrosoftResearch.Infer.Distributions
Assembly: Infer.Runtime (in Infer.Runtime.dll) Version: 2.5.30417.0 (2.5.30417.0)


The distribution is p(x) = x^(a-1)*exp(-x*b)*b^a/Gamma(a). In this code, the a parameter is called the "Shape" and the b parameter is called the "Rate". The distribution is sometimes also parameterized by (shape,scale) where scale = 1/rate. The mean of the distribution is shape/rate and the variance is shape/rate^2.

Special cases: When the shape is 1 and rate is 0, the distribution is uniform. When the shape is infinity, the distribution is a point mass and the density is delta(x-Point) where the Point property gives the mean. When a <= 0 or b <= 0 the b^a/Gamma(a) term is dropped.

See Also