`PsiGamma (a,β,...)`

PsiGamma (α,β) is a flexible distribution with a finite lower bound and decreasing values.  PsiExponential, PsiErlang, and PsiChi­Square are special cases of PsiGamma, as explained below.  The Gamma distribution is often used to model the time between events that occur with a constant average rate.

When α = 1, the Gamma distribution is the same as an Exponential distribution. If the parameter α is integer, then the Gamma distribution is the same as the Erlang distribution. The Gamma distribution with α = a/2, β = 2 is the same as a Chi Square distribution with parameter a (a degrees of freedom).

If X1, X2, …Xm are independent random variables with Xi  ~ PsiGamma (αi,β), then their sum also has a Gamma distribution with parameters (α1 + α2 + …+ αm ,β). Additionally, the Gamma distribution approaches a normal distribution with the same mean and standard deviation as the parameter α approaches infinity.

Alternate Formulation:  PsiGammaAlt

PsiGammaAlt is the PsiGamma distribution defined through alternative arguments.  Two parameters are required and both must be chosen from the following list:  percentile1, percentile2, mean, var, shape or scale. PsiGammaAlt is not supported in Analytic Solver Cloud app.