Unit-Chen distribution and its quantile regression model with applications - Ammar M. Sarhan (Scientific African)
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.