Unit Distributions: A General Framework, Some Special Cases, and the Regression Unit-Dagum Models

Abstract

In this work, we propose a general framework for models with support in the unit interval, which is obtained using the technique of random variable transformations. For this class, the general expressions of distribution and density functions are given, together with the principal characteristics, such as quantiles, moments, and hazard and reverse hazard functions. It is possible to verify that different proposals already present in the literature can be seen as particular cases of this general structure by choosing a suitable transformation. Moreover, we focus on the class of unit-Dagum distributions and, by specifying two different kinds of transformations, we propose the type I and type II unit-Dagum distributions. For these two models, we first consider the possibility of expressing the distribution in terms of indicators of interest, and then, through the regression approach, relate the indicators and covariates. Finally, some applications using data on the unit interval are reported.

Laplace-Logistic Unit Distribution with Application in Dynamic and Regression Analysis

“…On the other hand, modeling with unit distributions differs from common stochastic modeling procedures, primarily due to the limitation of data within (0, 1) interval. Although the procedure for creating unit distributions can be given in a general form [14], the most common approach is based on continuous transformations of distributions defined on infinite intervals into a unit interval (as some recent results, see e.g. [15]- [23]).…”