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Generalized Gamma Distribution

docs/tutorial:stats:continuous_gengamma

A general probability form that reduces to many common distributions. There are two shape parameters $a > 0$ and $c \neq = 0$ . The support is $x \geq 0$ .

where $γ$ is the lower incomplete gamma function, $γ (s, x) = \int_{0}^{x} t^{s - 1} e^{- t} d t$ .

Special cases are Weibull $(a = 1)$ , half-normal $(a = 1/2, c = 2)$ and ordinary gamma distributions $c = 1.$ If $c = - 1$ then it is the inverted gamma distribution.

h [X] = a - a Ψ (a) + \frac{1}{c} Ψ (a) + lo g Γ (a) - lo g ∣ c ∣ .

Implementation: scipy.stats.gengamma