Study of a Modified Kumaraswamy Distribution

In this article, a structural modification of the Kumaraswamy distribution yields a new two-parameter distribution defined on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mn>...

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Autores principales:	Rashad A. R. Bantan, Christophe Chesneau, Farrukh Jamal, Mohammed Elgarhy, Waleed Almutiry, Amani Abdullah Alahmadi
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	Kumaraswamy distribution logarithmic transformation moments quantile real data applications Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/bc98f10077e140629454feeca3e5406a
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spelling	oai:doaj.org-article:bc98f10077e140629454feeca3e5406a2021-11-11T18:21:37ZStudy of a Modified Kumaraswamy Distribution10.3390/math92128362227-7390https://doaj.org/article/bc98f10077e140629454feeca3e5406a2021-11-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/21/2836https://doaj.org/toc/2227-7390In this article, a structural modification of the Kumaraswamy distribution yields a new two-parameter distribution defined on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></semantics></math></inline-formula>, called the modified Kumaraswamy distribution. It has the advantages of being (i) original in its definition, mixing logarithmic, power and ratio functions, (ii) flexible from the modeling viewpoint, with rare functional capabilities for a bounded distribution—in particular, N-shapes are observed for both the probability density and hazard rate functions—and (iii) a solid alternative to its parental Kumaraswamy distribution in the first-order stochastic sense. Some statistical features, such as the moments and quantile function, are represented in closed form. The Lambert function and incomplete beta function are involved in this regard. The distributions of order statistics are also explored. Then, emphasis is put on the practice of the modified Kumaraswamy model in the context of data fitting. The well-known maximum likelihood approach is used to estimate the parameters, and a simulation study is conducted to examine the performance of this approach. In order to demonstrate the applicability of the suggested model, two real data sets are considered. As a notable result, for the considered data sets, statistical benchmarks indicate that the new modeling strategy outperforms the Kumaraswamy model. The transmuted Kumaraswamy, beta, unit Rayleigh, Topp–Leone and power models are also outperformed.Rashad A. R. BantanChristophe ChesneauFarrukh JamalMohammed ElgarhyWaleed AlmutiryAmani Abdullah AlahmadiMDPI AGarticleKumaraswamy distributionlogarithmic transformationmomentsquantilereal data applicationsMathematicsQA1-939ENMathematics, Vol 9, Iss 2836, p 2836 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Kumaraswamy distribution logarithmic transformation moments quantile real data applications Mathematics QA1-939
spellingShingle	Kumaraswamy distribution logarithmic transformation moments quantile real data applications Mathematics QA1-939 Rashad A. R. Bantan Christophe Chesneau Farrukh Jamal Mohammed Elgarhy Waleed Almutiry Amani Abdullah Alahmadi Study of a Modified Kumaraswamy Distribution
description	In this article, a structural modification of the Kumaraswamy distribution yields a new two-parameter distribution defined on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></semantics></math></inline-formula>, called the modified Kumaraswamy distribution. It has the advantages of being (i) original in its definition, mixing logarithmic, power and ratio functions, (ii) flexible from the modeling viewpoint, with rare functional capabilities for a bounded distribution—in particular, N-shapes are observed for both the probability density and hazard rate functions—and (iii) a solid alternative to its parental Kumaraswamy distribution in the first-order stochastic sense. Some statistical features, such as the moments and quantile function, are represented in closed form. The Lambert function and incomplete beta function are involved in this regard. The distributions of order statistics are also explored. Then, emphasis is put on the practice of the modified Kumaraswamy model in the context of data fitting. The well-known maximum likelihood approach is used to estimate the parameters, and a simulation study is conducted to examine the performance of this approach. In order to demonstrate the applicability of the suggested model, two real data sets are considered. As a notable result, for the considered data sets, statistical benchmarks indicate that the new modeling strategy outperforms the Kumaraswamy model. The transmuted Kumaraswamy, beta, unit Rayleigh, Topp–Leone and power models are also outperformed.
format	article
author	Rashad A. R. Bantan Christophe Chesneau Farrukh Jamal Mohammed Elgarhy Waleed Almutiry Amani Abdullah Alahmadi
author_facet	Rashad A. R. Bantan Christophe Chesneau Farrukh Jamal Mohammed Elgarhy Waleed Almutiry Amani Abdullah Alahmadi
author_sort	Rashad A. R. Bantan
title	Study of a Modified Kumaraswamy Distribution
title_short	Study of a Modified Kumaraswamy Distribution
title_full	Study of a Modified Kumaraswamy Distribution
title_fullStr	Study of a Modified Kumaraswamy Distribution
title_full_unstemmed	Study of a Modified Kumaraswamy Distribution
title_sort	study of a modified kumaraswamy distribution
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/bc98f10077e140629454feeca3e5406a
work_keys_str_mv	AT rashadarbantan studyofamodifiedkumaraswamydistribution AT christophechesneau studyofamodifiedkumaraswamydistribution AT farrukhjamal studyofamodifiedkumaraswamydistribution AT mohammedelgarhy studyofamodifiedkumaraswamydistribution AT waleedalmutiry studyofamodifiedkumaraswamydistribution AT amaniabdullahalahmadi studyofamodifiedkumaraswamydistribution
_version_	1718431908020355072

Study of a Modified Kumaraswamy Distribution

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