1. Flexible CDF-quantile distributions on the closed unit interval, with software and applications.
- Author
-
Smithson, Michael and Shou, Yiyun
- Subjects
- *
APPLICATION software , *RANDOM variables , *ESTIMATION bias , *PARAMETER estimation , *QUANTILE regression , *GAS separation membranes - 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. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF