A new class of unit models with a quantile regression approach applied to contamination data

Abstract

In this paper, we introduce a new class of unit models defined on the open unit interval. Through the reparameterization of the model, the location parameter can be interpreted as a quantile of the distribution. Furthermore, we can assess the impact of explanatory variables within the conditional quantiles of the dependent variable, offering an alternative to the Kumaraswamy quantile regression model. We engage in quantile regression and apply it to two instances of environmental data. We evaluate the effectiveness of the newly introduced models in scenarios both with and without covariates, drawing comparisons with results yielded by the Kumaraswamy regression model. The proposed method has been implemented in an R package.