Uma nova classe de distribuições unitárias baseada na família Weibull estendida com aplicação em dados eleitorais

Abstract

We propose a family of distributions so-called the new unit extended Weibull family (NWEU). It is derived from a transformation in an extended Weibull random variable. Six NWEU submodels are studied, namely: i) exponential unitary exponential distribution; ii) unit Gompertz distribution; iii) unit half-logistic distribution; iv) unit Lomax distribution; v) unit Nadarajah-Haghighi distribution and vi) Unit Rayleigh distribution. We propose a quantileparameterization for the new family. The maximum likelihood estimators (MLEs) are presented. A Monte Carlo study is performed to evaluate the behavior of the MLEs of unit Rayleigh and unit Gompertz. We note that the unit Rayleigh MLE has closed-form and is approximately unbiased MLE, even for small samples. Finally, the NWEU submodels are adjusted to the proportion of the valid votes for the second round Brazilian presidential elections, considering the year 2018 and the northeast region. We focus on this region since it is the second-largest electoral site in Brazil. Besides, this is the only Brazilian region where the elected president did not receive the majority of electoral votes. The application shows the superiority of the new family when compared with other usual unit models, such as the Beta, Kumaraswamy, and unit gamma distributions.