Here is a generalized gamma distribution. 

https://github.com/jlapeyre/GenGammaDist.jl

https://en.wikipedia.org/wiki/Generalized_gamma_distribution

Only rand() and mean() are implemented, and again no tests. This depends on 
Distributions. The authors of Distributions may want to include something 
like this. The parameters may be chosen  to get the Amoroso distribution 
(inverse generalized gamma distribution) mentioned in the Wikipedia article.

John



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