A New Extended Cosine—G Distributions for Lifetime Studies

Mustapha Muhammad, Rashad A. R. Bantan, Lixia Liu, Christophe Chesneau, Muhammad H. Tahir, Farrukh Jamal and Mohammed Elgarhy
Additional contact information
Mustapha Muhammad: School of Mathematical Sciences, Hebei Normal University, Shijiazhuang 050024, China
Rashad A. R. Bantan: Department of Marine Geology, Faculty of Marines Science, King AbdulAziz University, Jeddah 21551, Saudi Arabia
Lixia Liu: School of Mathematical Sciences, Hebei Normal University, Shijiazhuang 050024, China
Christophe Chesneau: Department of Mathematics, Université de Caen, LMNO, Campus II, Science 3, 14032 Caen, France
Muhammad H. Tahir: Department of Statistics, The Islamia University of Bahawalpur, Punjab 63100, Pakistan
Farrukh Jamal: Department of Statistics, The Islamia University of Bahawalpur, Punjab 63100, Pakistan
Mohammed Elgarhy: The Higher Institute of Commercial Sciences, Al Mahalla Al Kubra, Algarbia 31951, Egypt

Mathematics, 2021, vol. 9, issue 21, 1-29

Abstract: 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.

Keywords: trigonometric distributions; moments; entropy; maximum likelihood estimation; least-square estimation; percentile estimation; Bayes estimation; stress–strength parameter (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

Downloads: (external link)
https://www.mdpi.com/2227-7390/9/21/2758/pdf (application/pdf)
https://www.mdpi.com/2227-7390/9/21/2758/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:9:y:2021:i:21:p:2758-:d:668610

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().