The Unit-Gompertz Quantile Regression Model for the Bounded Responses

Abstract

ABSTRACT This paper proposes a regression model for the continuous responses bounded to the unit interval which is based on the unit-Gompertz distribution as an alternative to quantile regression models based on the unit-Birnbaum-Saunders, unit-Weibull, L-Logistic, Kumaraswamy and Johnson SB distributions. Re-parameterizing the unit-Gompertz distribution as a function of its quantile allows us to model the effect of covariates across the entire response distribution, rather than only at the mean. Our proposal sometimes outperforms the other distributions available in the literature. These discoveries are provided by Monte Carlo simulations and one application using a real data set. An R package, including parameter estimation, model checking as well as density, cumulative distribution, quantile and random number generating functions of the unit-Gompertz distribution are developed and can be readily used in applications.