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·       Format:

Gamma(Location, Scale, Shape) or Gamma(L,β, α)

·       Probability density function:

f(x)=\frac{\beta^{-\alpha} x^{\alpha-1}exp \bigg( - x/ \beta \bigg)}{\Gamma(\alpha )}

where  \Gamma(\bullet)is a Gamma Function 

·       Cumulative distribution function:

No closed form

·       Parameter restrictions:

a > 0, β > 0

·       Domain: 

x ≥ 0

·       Mean:

αβ

·       Mode: 

β(α - 1)                        if α ≥ 1

0                                  if α < 1

·       Variance:

αβ2

 

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