Directional Gaussian Hypergeometric Beta Distributions and their uses in Contaminated Binary Sampling

Abstract

We examine the Gaussian hypergeometric beta distribution and look at the effect of having an additional term in the density kernel relative to the standard beta distribution. We reparameterise and classify this distribution into left and right directional variants using parameters that give a simple and symmetrical representation of the directional push/pull from this additional term in the density kernel. We examine the properties of the directional variants and their uses in contaminated binary sampling using Bayesian inference. We find that the Gaussian hypergeometric beta distribution arises as the appropriate posterior distribution for inference in certain kinds of contaminated binary models and that the directional parameterisation aids in representation of the resulting Bayesian models. We derive a broad range of properties and computational methods for the directional variants of the distribution.