Gamma distribution
In probability theory and statistics, the
gamma distribution is a two-parameter family of continuous probability distributions. The common exponential distribution and chi-squared distribution are special cases of the gamma distribution. There are three different parametrizations in common use: ▪ With a shape parameter
k and a scale parameter θ. ▪ With a shape parameter
α =
k and an inverse scale parameter β = 1/θ, called a rate parameter. ▪ With a shape parameter
k and a mean parameter μ =
k/β. In each of these three forms, both parameters are positive real numbers. The parameterization with
k and θ appears to be more common in econometrics and certain other applied fields, where e.g. the gamma distribution is frequently used to model waiting times. For instance, in life testing, the waiting time until death is a random variable that is frequently modeled with a gamma distribution.