The unit generalized half-normal quantile regression model: formulation, estimation, diagnostics, and numerical applications

In this paper, we propose and derive a new regression model for response variables defined on the open unit interval. By reparameterizing the unit generalized half-normal distribution, we get the interpretation of its location parameter as being a quantile of the distribution. In addition, we can evaluate effects of the explanatory variables in the conditional quantiles of the response variable as an alternative to the Kumaraswamy quantile regression model. The suitability of our proposal is demonstrated with two simulated examples and two real applications. For such data sets, the obtained fits of the proposed regression model are compared with that provided by a Kumaraswamy regression model.

Automated summary

This paper proposes and derives a new regression model for response variables defined on the open unit interval. By reparameterizing a distribution, the interpretation of its location parameter is obtained. The effects of explanatory variables in the conditional quantiles of the response variable are evaluated as an alternative method. The suitability of the proposal is demonstrated through simulations and real applications.