After making the assumption that monetary losses could be well represented by a gamma distribution (Boland, 2007), mostly negatively skewed, and being interested in loss ratios (ie. lost value / total value), I performed a number of simulations sampling from a gamma distribution. I constrained the shape and scale parameters in such a way that the minimum and maximum values that could be sampled lied between 0 and 1.
Later on, I realized I could have just sampled directly from a beta distribution given that it is already defined between 0 and 1 - thus representing directly the fact I was looking at loss ratios only.
But this then raised the question: given that both gamma and beta pdfs can take a range of similar "shapes" (based on the values of their parameters), is it equivalent to use a gamma distribution (by somewhat constraining the parameters) and a beta distribution?
I have been trying the understand the relationship between the 2 distributions, but apart from the fact that if X is gamma distributed with parameters (a,r) and Y is gamma distributed with parameters (b,r) then X/(X+Y) is beta distributed with parameters (a,b), I did not find anything I could relate to the case I am interested in.
Ref. Boland, Statistical and Probabilistic Methods in Actuarial Science (2007), CRC Press.