Bayesian inference for unit Gamma distribution

In this article, we develop Bayesian inference for the unit-Gamma (GU) distribution, initially introduced by Grassia (1977). This distribution is highly flexible, allowing it to take various forms within the interval (0,1), encompassing both symmetric and asymmetric shapes. Such flexibility makes it an attractive alternative to traditional distributions in this range, like the Kumaraswamy and beta models. We propose a parameterization based on quantiles, a particularly advantageous approach when dealing with datasets that include outliers, since the median, for instance, is a more robust estimator compared to the mean in such cases. Our work covers parameter estimation, model fit assessment, model comparison, and influence analysis. All procedures were implemented using Markov Chain Monte Carlo (MCMC) methods via Just Another Gibbs Sampling (JAGS) through the R2jags package in R, an open-source software. Furthermore, we demonstrate the effectiveness of this methodology by applying it to a real-world dataset, highlighting its practical utility.