Directional Gaussian Hypergeometric Beta Distributions and their uses in Contaminated Binary Sampling
Year: 2026
Type: article
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.
Author: Ben O’Neill
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,290
OpenAlex ID: W7123649191