I'd like to know whether starting from a Beta distribution and iterating it in the way described below I get a stationary (beta) distribution again.
More specifically this is the problem I am facing:
Start with a Beta(2,1.5) for each element "phi" drawn from this pdf there is associated another distribution from which we draw: Beta("phi"+1,1.5). Iterating n times, as n goes to inf, this procedure do we get back a stationary distribution. Is it beta?
I think the problem could be rephrased also as follows, let the original starting point Beta be B0, we get a distribution (not sure if it would be beta) B2 associated with a probability measure CB2 that maps from every borel set A contained in [0,1] the following value:
and so on for all iterations.