Trabalho de Conclusão de Curso de Especialização
Uma nova classe de distribuições unitárias baseada na família Weibull estendida com aplicação em dados eleitorais
Fecha
2020-03-17Autor
Mafalda, Charles Peixoto
Institución
Resumen
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.