A competitive family to the Beta and Kumaraswamy generators: Properties, Regressions and Applications.
Autor: | Cordeiro GM; Universidade Federal de Pernambuco, Departamento de Estatística, Avenida Professor Moraes Rego, s/n, Bairro Iputinga, 50670-901 Recife, PE, Brazil., Vasconcelos JCS; Universidade de São Paulo, Departamento de Ciências Exatas, Avenida Pádua Dias, 11, Bairro São Dimas, 13418-900 Piracicaba, SP, Brazil., Ortega EMM; Universidade de São Paulo, Departamento de Ciências Exatas, Avenida Pádua Dias, 11, Bairro São Dimas, 13418-900 Piracicaba, SP, Brazil., Marinho PRD; Universidade Federal da Paraíba, Departamento de Estatística, Cidade Universitária, s/n, Bairro Castelo Branco, 58054-900 João Pessoa, PB, Brazil. |
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Jazyk: | angličtina |
Zdroj: | Anais da Academia Brasileira de Ciencias [An Acad Bras Cienc] 2022 Jul 18; Vol. 94 (2), pp. e20201972. Date of Electronic Publication: 2022 Jul 18 (Print Publication: 2022). |
DOI: | 10.1590/0001-3765202220201972 |
Abstrakt: | We define two new flexible families of continuous distributions to fit real data by compoun-ding the Marshall-Olkin class and the power series distribution. These families are very competitive to the popular beta and Kumaraswamy generators. Their densities have linear representations of exponentiated densities. In fact, as the main properties of thirty five exponentiated distributions are well-known, we can easily obtain several properties of about three hundred fifty distributions using the references of this article and five special cases of the power series distribution. We provide a package implemented in R software that shows numerically the precision of one of the linear representations. This package is useful to calculate numerical values for some statistical measurements of the generated distributions. We estimate the parameters by maximum likelihood. We define a regression based on one of the two families. The usefulness of a generated distribution and the associated regression is proved empirically. |
Databáze: | MEDLINE |
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