Flexible CDF-quantile distributions on the closed unit interval, with software and applications

Michael Smithson and Yiyun Shou

Communications in Statistics - Theory and Methods, 2024, vol. 53, issue 11, 3876-3898

Abstract: This paper presents a flexible family of 2- and 3-parameter distributions whose support is the closed interval [0,1], with explicit density, cumulative density, and quantile functions. These distributions are suited to modeling quantiles, thereby expanding the toolbox of distributions for doubly-bounded random variables. The densities at the boundaries are determined by dispersion and skew parameters, and a third parameter exclusively influences location. The paper also discusses practical issues of parameter estimation and assesses estimation bias, Type I error-rate accuracy, and parameter-estimate collinearity. It also provides three examples of applications to real data using new packages implementing the distributions in R and Stata.

Date: 2024
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DOI: 10.1080/03610926.2023.2166352

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