A Quantile Regression Model for Bounded Responses Based on the Exponential-Geometric Distribution

Abstract

The paper first introduces a new two-parameter continuous probability distribution with bounded support from the extended exponential-geometric distribution. Closed-form expressions are given for the moments, moments of the order statistics and quantile function of the new law; it is also shown that the members of this family of distributions can be ordered in terms of the likelihood ratio order. The parameter estimation is carried out by the method of maximum likelihood and a closed-form expression is given for the Fisher information matrix, which is helpful for asymptotic inferences. Then, a new regression model is introduced by considering the proposed distribution, which is adequate for situations where the response variable is restricted to a bounded interval, as an alternative to the well-known beta regression model, among others. It relates the median response to a linear predictor through a link function. Extensions for other quantiles can be similarly performed. The suitability of this regression model is exemplified by means of a real data application.