I’m not very familiar with Distributions.jl, but from some experimenting I just did with the package I think it is safe to assume that the four-parameter distribution \mathrm{Beta}(\alpha, \beta, a, b), with support [a, b], can be defined in terms of the standard Beta distribution as (b - a) \times \mathrm{Beta}(\alpha, \beta) + a. (Please correct me if wrong.)