Novel Quantile Regression Model Using Extended Exponential-Geometric Distribution with Real Data Application

Abstract

In this research, we propose a quantile regression framework that accounts for the nature of the dependent variables that are restricted to the interval between 0 and 1, specifically through the utilization of the Unit Extended Exponential, Geometric (UEEG) distribution. The method is capable of capturing the effects of covariates at different quantiles of the distribution, thus enabling a more comprehensive representation of the changes in behavior across the entire range. We analyze the distribution characteristics of the model and recommend maximum likelihood parameter estimation. A simulation experiment is performed to test the properties of the proposed estimators at finite samples with respect to bias and MSE. The methodology is demonstrated through the application to a real data set in order to showcase its practical utility. The new framework is compared against the analogous ones based on Unit Exponential, Unit Extended Exponential, and Unit Lindley distributions using the Akaike information criterion (AIC), Bayesian information criterion (BIC), and  HannanQuinn information criterion (HQIC). The findings suggest that not only does the new model fit the data better, but it is also less biased and has a lower MSE, therefore, providing more flexibility for data restricted to a unit interval.