Table 1 Selected Extensions of the Generalized Gamma Distribution
From: Describing the Flexibility of the Generalized Gamma and Related Distributions
Distribution | CDF | Additional parameters |
|---|---|---|
Generalized Gamma | F GG (t) | n/a |
Beta GG | \( {F}_{BGG}(t)={F}_B\left({F}_{GG}(t)\right)=\frac{B\left({F}_{GG}(t);\theta, \tau \right)}{B\left(\theta, \tau \right)} \) | θ > 0 , τ > 0 |
Kumaraswamy GG | F KGG (t) = 1 − (1 − F GG (t)λ)φ | λ > 0 , φ > 0 |
Transmuted GG | F TGG (t) = (1 + λ)F GG (t) − λF GG (t)2 | −1 ≤ λ ≤ 1 |
Marshall-Olkin GG | \( {F}_{MOGG}(t)=1-\frac{\alpha \left(1-{F}_{GG}(t)\right)}{1-\left(1-\alpha \right)\left(1-{F}_{GG}(t)\right)} \) | α > 0 |