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

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  • Michael Smithson
  • Yiyun Shou

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.

Suggested Citation

  • Michael Smithson & Yiyun Shou, 2024. "Flexible CDF-quantile distributions on the closed unit interval, with software and applications," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 53(11), pages 3876-3898, June.
    • Handle: RePEc:taf:lstaxx:v:53:y:2024:i:11:p:3876-3898
    DOI: 10.1080/03610926.2023.2166352
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