Gamma Distribution |
(continuous probability dist for equations) |
Usage: |
GammaDist (x, α, β) |
Definition: |
x^(α-1) exp(-x/ β) / (gamma(α) β ^ α) = exp[(α-1)log(x) - x/ β - log(gamma(α)) - α log(β)] |
Parameters: |
α is shape β is scale |
Required: |
α > 0 β > 0 |
Support: |
x ⋝ 0 |
Moments: |
μ = α β σ = β sqrt (α) γ1 = 2 / sqrt (α) β2 = 3 + 6 / α |
If events occur by a Poisson process, then the time required for the occurrence of α events is described by the gamma distribution (where β is the average time between events).
For α = 1, this is the exponential distribution with λ = 1 / β. For β = 2, this is the chi-square distribution with degrees of freedom ν = 2α.
The Erlang distribution is a special case of the gamma distribution in which β = 1 and α = n (which is an integer).
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