Betapriorin
Betapriorin is a hypothetical probability distribution proposed as a flexible prior in Bayesian inference, intended for modeling a probability parameter that lies in the interval [0, 1]. It is described as a generalization of the Beta distribution, introduced to encode prior beliefs that cannot be fully captured by the two-parameter Beta form alone. In this framing, betapriorin retains the domain of the Beta distribution but adds an extra shaping mechanism to adjust tails or central concentration beyond what alpha and beta control.
Mathematically, betapriorin is defined on the unit interval with a density of the form proportional to x^(α−1)
Properties of betapriorin depend on the likelihood and the chosen shape function g. In general, conjugacy to
Applications of betapriorin appear in theoretical or applied Bayesian statistics where enhanced prior flexibility is desired