A New Extended Cosine—G Distributions for Lifetime Studies

In this article, we introduce a new extended cosine family of distributions. Some important mathematical and statistical properties are studied, including asymptotic results, a quantile function, series representation of the cumulative distribution and probability density functions, moments, moments...

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Autores principales:	Mustapha Muhammad, Rashad A. R. Bantan, Lixia Liu, Christophe Chesneau, Muhammad H. Tahir, Farrukh Jamal, Mohammed Elgarhy
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	trigonometric distributions moments entropy maximum likelihood estimation least-square estimation percentile estimation Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/c358b4fa88bf4d45bc1a204576bf2fa0
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spelling	oai:doaj.org-article:c358b4fa88bf4d45bc1a204576bf2fa02021-11-11T18:18:10ZA New Extended Cosine—G Distributions for Lifetime Studies10.3390/math92127582227-7390https://doaj.org/article/c358b4fa88bf4d45bc1a204576bf2fa02021-10-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/21/2758https://doaj.org/toc/2227-7390In this article, we introduce a new extended cosine family of distributions. Some important mathematical and statistical properties are studied, including asymptotic results, a quantile function, series representation of the cumulative distribution and probability density functions, moments, moments of residual life, reliability parameter, and order statistics. Three special members of the family are proposed and discussed, namely, the extended cosine Weibull, extended cosine power, and extended cosine generalized half-logistic distributions. Maximum likelihood, least-square, percentile, and Bayes methods are considered for parameter estimation. Simulation studies are used to assess these methods and show their satisfactory performance. The stress–strength reliability underlying the extended cosine Weibull distribution is discussed. In particular, the stress–strength reliability parameter is estimated via a Bayes method using gamma prior under the square error loss, absolute error loss, maximum a posteriori, general entropy loss, and linear exponential loss functions. In the end, three real applications of the findings are provided for illustration; one of them concerns stress–strength data analyzed by the extended cosine Weibull distribution.Mustapha MuhammadRashad A. R. BantanLixia LiuChristophe ChesneauMuhammad H. TahirFarrukh JamalMohammed ElgarhyMDPI AGarticletrigonometric distributionsmomentsentropymaximum likelihood estimationleast-square estimationpercentile estimationMathematicsQA1-939ENMathematics, Vol 9, Iss 2758, p 2758 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	trigonometric distributions moments entropy maximum likelihood estimation least-square estimation percentile estimation Mathematics QA1-939
spellingShingle	trigonometric distributions moments entropy maximum likelihood estimation least-square estimation percentile estimation Mathematics QA1-939 Mustapha Muhammad Rashad A. R. Bantan Lixia Liu Christophe Chesneau Muhammad H. Tahir Farrukh Jamal Mohammed Elgarhy A New Extended Cosine—G Distributions for Lifetime Studies
description	In this article, we introduce a new extended cosine family of distributions. Some important mathematical and statistical properties are studied, including asymptotic results, a quantile function, series representation of the cumulative distribution and probability density functions, moments, moments of residual life, reliability parameter, and order statistics. Three special members of the family are proposed and discussed, namely, the extended cosine Weibull, extended cosine power, and extended cosine generalized half-logistic distributions. Maximum likelihood, least-square, percentile, and Bayes methods are considered for parameter estimation. Simulation studies are used to assess these methods and show their satisfactory performance. The stress–strength reliability underlying the extended cosine Weibull distribution is discussed. In particular, the stress–strength reliability parameter is estimated via a Bayes method using gamma prior under the square error loss, absolute error loss, maximum a posteriori, general entropy loss, and linear exponential loss functions. In the end, three real applications of the findings are provided for illustration; one of them concerns stress–strength data analyzed by the extended cosine Weibull distribution.
format	article
author	Mustapha Muhammad Rashad A. R. Bantan Lixia Liu Christophe Chesneau Muhammad H. Tahir Farrukh Jamal Mohammed Elgarhy
author_facet	Mustapha Muhammad Rashad A. R. Bantan Lixia Liu Christophe Chesneau Muhammad H. Tahir Farrukh Jamal Mohammed Elgarhy
author_sort	Mustapha Muhammad
title	A New Extended Cosine—G Distributions for Lifetime Studies
title_short	A New Extended Cosine—G Distributions for Lifetime Studies
title_full	A New Extended Cosine—G Distributions for Lifetime Studies
title_fullStr	A New Extended Cosine—G Distributions for Lifetime Studies
title_full_unstemmed	A New Extended Cosine—G Distributions for Lifetime Studies
title_sort	new extended cosine—g distributions for lifetime studies
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/c358b4fa88bf4d45bc1a204576bf2fa0
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A New Extended Cosine—G Distributions for Lifetime Studies

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