Regressão Weibull truncada modal para modelar diferenças entre taxas ou proporções

Abstract

In this work, a study based on the truncated Weibull distribution is developed. Truncation is performed in the interval (0,2), referred to as right truncation. However, in order to analyze data on differences between rates or proportions, a transformation is suggested to obtain a new distribution whose support set belongs to the interval (−1,1). Furthermore, this distribution has been parameterized in terms of mode and shape parameters, and it is called the truncated Modal Weibull distribution (TMW). A new modal regression model based on the WTM distribution with regression structures for the parameters is proposed, and the chosen estimation method is maximum likelihood. A simulation study was conducted using the Monte Carlo method to evaluate the performance of the maximum likelihood estimators for different scenarios and regression structures. Furthermore, analytical expressions for the Fisher information matrix were obtained. Finally, three applications of the WTM regression model are presented, two of which are for electoral data from Brazil and the United States of America and one referring to a promotion exam for the fire department.