Document Type : original

Author

• Lazhar BENKHELIFA

univ biskra

Abstract

The paper suggests a novel model defined on the unit interval, termed the unit linear exponential distribution, constructed via an inversion of the exponential function. The proposed model contains the unit exponential and the unit Rayleigh distributions as special submodels. Fundamental properties of the introduced distribution are discussed which are stochastic ordering property, quantile function, incomplete moments, moments, probability weighted moment, order statistics, stochastic orderings, stress strength reliability, and Tsallis and Renyi entropies. The distribution has two unknown parameters, which are estimated utilizing the following methods: maximum likelihood, maximum product spacing, least and weighted least squares, Cramér-von Mises, and Anderson-Darling. The behavior of these estimators is assessed through a simulation study. Furthermore, the paper develops a novel quantile regression model based on suggested distribution, which is shown to be a good alternative to existing models like the Kumaraswamy, beta, and unit Chen quantile regression models. We estimate the parameters of the regression model utilizing maximum likelihood. Two well-known real data applications are given to prove the modeling capability of the newly suggested distribution and quantile regression model.

Keywords

• Unit distribution
• linear exponential distribution
• estimation methods
• Monte Carlo simulations
• Data analysis

Main Subjects

• Statistical Computing