The expected value and standard deviation of a gamma random variable X are:
E(X) = kθ and
Var(X) = kθ2.
In case k is an integer, the gamma distribution is an Erlang distribution (so named in honor of A.K. Erlang) and is the probability distribution of the waiting time of the kth "arrival" in a one-dimensional Poisson process with intensity 1/θ. If k is a half-integer and θ = 2, then the gamma distribution is a chi-square distribution with 2k degrees of freedom.