Unit-Chen distribution and its quantile regression model with applications

Abstract

The need for new statistical distributions that can effectively fit real datasets on the unit interval is crucial in data analysis. This article introduces a new family of statistical distributions on the unit interval, called the unit-Chen distribution, derived from the two-parameter Chen distribution. The statistical properties of the proposed distribution are discussed, along with a quantile regression model based on the unit-Chen distribution. Both maximum likelihood and Bayesian procedures are used to estimate the model’s parameters. For the Bayesian approach, two methods of approximate Bayesian computation (ABC) are employed: the accept-reject (AR) method and sampling importance resampling (SIR) method. A simulation study is provided to investigate the properties of the maximum likelihood method applied. Based on well-known diagnostic tests, the simulation data presented in this paper is appropriate. To demonstrate the applicability of the proposed models, real-life datasets (four using unit-Chen and one using unit-Chen regression) are analyzed. The performance of the proposed models is compared with other well-known distributions. The comparison results indicate that the unit-Chen and unit-Chen regression models fit the data better than the competitive models applied in this study.