Bayesian inference for zero-and/or-one augmentedunit-gamma

In this paper, we propose a new distribution based on a mixture of the unit-gamma distribution with a degenerate distribution at (c) (0 or1) or with a Bernoulli distribution. This novel approach is particularlyuseful for addressing excess zeros and/or ones in the data with limitedsupport in ( 0 , 1 ) .Our approach considers Bayesian parameter estimation, residual, and influence analysis, as well as model comparison methods. We illustratethe theory by applying it to a real-world problem, with all posteriorquantities obtained using Markov Chain Monte Carlo (MCMC) methods.