A competitive family to the Beta and Kumaraswamy generators: Properties, Regressions and Applications

A competitive family to the Beta and Kumaraswamy generators: Properties, Regressions and Applications

Abstract 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.

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Main Authors: CORDEIRO,GAUSS M., VASCONCELOS,JULIO CEZAR S., ORTEGA,EDWIN M.M., MARINHO,PEDRO RAFAEL D.
Format: Digital revista
Language:English
Published: Academia Brasileira de Ciências 2022
Online Access:http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652022000300301
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spelling oai:scielo:S0001-376520220003003012022-07-14A competitive family to the Beta and Kumaraswamy generators: Properties, Regressions and ApplicationsCORDEIRO,GAUSS M.VASCONCELOS,JULIO CEZAR S.ORTEGA,EDWIN M.M.MARINHO,PEDRO RAFAEL D. generating function Marshall–Olkin family maximum likelihood moment distribution Abstract 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.info:eu-repo/semantics/openAccessAcademia Brasileira de CiênciasAnais da Academia Brasileira de Ciências v.94 n.2 20222022-01-01info:eu-repo/semantics/articletext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652022000300301en10.1590/0001-3765202220201972
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author CORDEIRO,GAUSS M.
VASCONCELOS,JULIO CEZAR S.
ORTEGA,EDWIN M.M.
MARINHO,PEDRO RAFAEL D.
spellingShingle CORDEIRO,GAUSS M.
VASCONCELOS,JULIO CEZAR S.
ORTEGA,EDWIN M.M.
MARINHO,PEDRO RAFAEL D.
A competitive family to the Beta and Kumaraswamy generators: Properties, Regressions and Applications
author_facet CORDEIRO,GAUSS M.
VASCONCELOS,JULIO CEZAR S.
ORTEGA,EDWIN M.M.
MARINHO,PEDRO RAFAEL D.
author_sort CORDEIRO,GAUSS M.
title A competitive family to the Beta and Kumaraswamy generators: Properties, Regressions and Applications
title_short A competitive family to the Beta and Kumaraswamy generators: Properties, Regressions and Applications
title_full A competitive family to the Beta and Kumaraswamy generators: Properties, Regressions and Applications
title_fullStr A competitive family to the Beta and Kumaraswamy generators: Properties, Regressions and Applications
title_full_unstemmed A competitive family to the Beta and Kumaraswamy generators: Properties, Regressions and Applications
title_sort competitive family to the beta and kumaraswamy generators: properties, regressions and applications
description Abstract 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.
publisher Academia Brasileira de Ciências
publishDate 2022
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652022000300301
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