Do you have descriptive/typical examples for processes whose results are described by a beta distribution? So far i only have one:
You have a population of constant size with N individuals and you observe a single gene (or gene locus). The descendants in the next generation are drawn from a binomial distribution, so some individuals have several descendants, others have no dexcendants. The gene can mutate at a rate u (for example blue eyes become brown eyes in 10^-5 cases you draw an individual with blue eyes). Thae rate at which brown eyed individuals have blue eyed descendants ist the same.
The beta distribution describes how likely it is to find X% of the individuals having a ceratian eye colour. Thereby 2*N*u is the value for both parameters of the beta distribution.
Do you have mor examples. For which things is the beta distribution used?