Question

define gamma distributionm
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Answer 1

Answer:

In probability theory and statistics, the gamma distribution is a two-parameter family of continuous probability distributions. The exponential distribution, Erlang 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 = kθ = α/β.

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

The gamma distribution is the maximum entropy probability distribution (both with respect to a uniform base measure and with respect to a 1/x base measure) for a random variable X for which E[X] = kθ = α/β is fixed and greater than zero, and E[ln(X)] = ψ(k) + ln(θ) = ψ(α) − ln(β) is fixed (ψ is the digamma function).[1]

Answer 2

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