The expected value and standard deviation of a gamma random variable *X* are:

E(X) = kθ and

Var(X) = kθ^{2}.

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 *k*th "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.