A flexible procedure for formulating probability distributions on the unit interval with applications. Issue 3 (1st February 2020)

• Record Type: Journal Article
• Authors: Rodrigues, Josemar; Bazán, Jorge L.; Suzuki, Adriano K.
• Is Part Of: Communications in statistics. Volume 49:Issue 3(2020)
• Page Start: 738
• Page End: 754
• Publication Date: 2020-02-01
• Subjects: Bayesian method -- Beta distribution -- bounded support -- composite probability distribution -- GAMLSS -- quantile function -- regression models -- Rstan; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2018.1549254
• Languages: English
• ISSNs: 0361-0926

Abstract

Abstract: In this paper, we present a flexible mechanism for constructing probability distributions on a bounded intervals which is based on the composition of the baseline cumulative probability function and the quantile transformation from another cumulative probability distribution. In particular, we are interested in the (0, 1) intervals. The composite quantile family of probability distributions contains many models that have been proposed in the recent literature and new probability distributions are introduced on the unit interval. The proposed methodology is illustrated with two examples to analyze a poverty dataset in Peru from the Bayesian paradigm and Likelihood points of view.