A New Extended Cosine—G Distributions for Lifetime Studies

Mathematics

Rashad A. R. Bantan¹  Christophe Chesneau²  Farrukh Jamal³  Muhammad H. Tahir³  Lixia Liu⁴  Mustapha Muhammad⁴  Mohammed Elgarhy⁵ 

[1] Department of Marine Geology, Faculty of Marines Science, King AbdulAziz University, Jeddah 21551, Saudi Arabia;Department of Mathematics, Université de Caen, LMNO, Campus II, Science 3, 14032 Caen, France;Department of Statistics, The Islamia University of Bahawalpur, Punjab 63100, Pakistan;School of Mathematical Sciences, Hebei Normal University, Shijiazhuang 050024, China;The Higher Institute of Commercial Sciences, Al Mahalla Al Kubra, Algarbia 31951, Egypt;

关键词: trigonometric distributions;    moments;    entropy;    maximum likelihood estimation;    least-square estimation;    percentile estimation;   

DOI  :  10.3390/math9212758

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown