Generalized Gamma Distribution
X ~ GenGamma(a, c, β)
Unifying / Flexible-Hazard Family • Published July 22, 2026
E.W. Stacy's 1962 unifying capstone for this Lifetime/Survival batch, playing the same role the already-published Generalized Normal played for the Laplace/Normal/Uniform: a=1 gives the already-published Weibull exactly, c=1 gives the already-published Gamma exactly, and a=c=1 gives the already-published Exponential exactly (all three ties confirmed to 2.8e-17). No closed-form maximum-likelihood estimator for any of the three parameters.
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About This Reference Sheet
E.W. Stacy's 1962 unifying capstone for this Lifetime/Survival batch, playing the same role the already-published Generalized Normal played for the Laplace/Normal/Uniform: a=1 gives the already-published Weibull exactly, c=1 gives the already-published Gamma exactly, and a=c=1 gives the already-published Exponential exactly (all three ties confirmed to 2.8e-17). No closed-form maximum-likelihood estimator for any of the three parameters.
Support
x ∈ (0, ∞)
Parameters
a > 0 (shape), c > 0 (shape), β > 0 (scale)