Classical and Bayesian analysis on the rectangular beta distribution

Abstract

This paper deals with the problem of working with data expressed in proportions that contain extreme values. The general objective of the study was to study the properties, estimate and apply to real data the Beta Rectangular distribution model, which has been specifically built to carry out the statistical analysis of data expressed in proportions that contain extreme values. The study was carried out from the classical and Bayesian point of view. For the implementation of the Bayesian inference, Markov Chain Monte Carlo (MCMC) simulations were considered. In order to evaluate the robustness of the Beta Rectangular distribution model, it was compared with the Beta distribution model both by classical inference and by Bayesian inference, and simulation studies were carried out under different scenarios generated by variations in the value of the parameters. of the distribution. Simulation studies have shown that the Beta Rectangular distribution model is more robust than the Beta distribution model. In the complementary case, that is, when the data does not include extreme values, there is an alternation between the Beta Rectangular and Beta models in relation to which of them best fits the data. It is concluded that the Beta Rectangular distribution model presents adequate properties to work with data sets expressed in proportions, restricted to the interval [0, 1] of the real line, and that present extreme values. When this situation occurs, the Beta Rectangular distribution model has a better fit to the data than the Beta distribution model.