Hello everyone,

I am trying to define a PERT distribution "by hand"  by transforming a classic beta distribution - as I would like to understand where the shape parameter (default value of 4) comes from in the mc2d package.

The help page says
"The PERT distribution is a beta distribution extended to the domain [min, max] with mean mu = (min + shape * mode + max)/(shape + 2)"

At the same time, we know that a 4 parameter beta distribution's mean can be expressed as
mu = (alpha * max + beta * min)/(alpha + beta)

So using the equality between the 2 expressions of mu I can find the shape parameter as a function of alpha and beta. But if I want to set the shape parameter to 4, how do I define alpha and beta? All I know is that my distribution is unimodal and positively skewed.

In other words, is there a way to find the values of the 2 shape parameters of the "underlying beta distribution" by setting the min, max, mode, maybe some constraints on alpha and beta (alpha < beta;  >1) and R-defined unique shape parameter?

I think maybe I am missing something here.

Many thanks




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