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The Gamma Distribution





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The gamma distribution is a two-parameter family of continuous probability distributions.

The exponential distribution, the Erlang distribution and the chi-square distribution are special cases of the gamma distribution.

There are two different commonly used parametrizations:

1. With a shape parameter k and a scale parameter θ.

2. With a shape parameter α = k and an inverse scale parameter β = 1/θ which is called rate parameter.

In each of these forms, both parameters are positive real numbers.

The gamma distribution is the maximum entropy probability distribution for a random variable X for which E[X] = kθ = α/β is fixed and greater than zero and E[ln] = ψ + ln = ψ − ln fixed rule .











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