I'm posting this partially to get a question answered and partially so someone else might find it later and save them the headache.
I am trying to create a beta-pert distribution in NetLogo by following the formula here from Epix Analytics
I've created an Beta(Alpha1, alpha2) distribution using the transformation from a gamma distbutiotn here on the Beta distribution wiki page:
The code that I've created is:
to pert let mu ((a + 4 * b + c) / 6) let alpha1 ((mu - a ) * (2 * b - a - c)) / ((b - mu) * (c - a)) let alpha2 (alpha1 * (c - mu)) / (mu - a) let x (random-gamma alpha1 1) let y (random-gamma alpha2 1) let beta-output (x / (x + y)) let output beta-output * (c - a) + a show output end
My question is about the Wikipedia page's transformation from a Gamma distribution to a Beta distribution. It has a theta as the second part of the gamma distrbution but doesnt ever define what that is. I took it as a placeholder and as long as theta is the same for both X and Y, would not affect the outcome. I've played with different theta values with no visible change in the distribution. Is this a correct assumption?