Gamma distribution

In probability theorystatistics,gamma distribution iscontinuous probability distribution withprobability density function definedx > 0 that can be expressedterms ofgamma function as follows:

where k >0 isshape parameterθ > 0 isscale parameter ofgamma distribution.

The expected valuestandard deviation ofgamma random variable X are:

E(X) = kθ and

Var(X) = kθ².

In case kan integer,gamma distributionan Erlang distribution (so namedhonorA.K. Erlang)isprobability distribution ofwaiting time ofkth "arrival" inone-dimensional Poisson processintensity 1/θ. If k ishalf-integerθ = 2, thengamma distribution ischi-square distribution2k degreesfreedom.