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.
Highlights
In various practical analyses, the choice of an appropriated statistical model is crucial
It was indicated that the maximum likelihood estimation (MLE), SLE, percentile estimation (PE), and Bayes estimation (BE) showed consistency, and their mean square error (MSE) decreased as the sample size increased; the bias of some parameters was negative in some cases
We provided an illustrative performance of the extended cosine-generated (ECSG) family through the extended cosine power (ECSP), extended cosine generalized half-logistic (ECSGHL), and extended cosine Weibull (ECSW) models using real datasets
Summary
Mustapha Muhammad 1,2, Rashad A. R. Bantan 3, Lixia Liu 1,*, Christophe Chesneau 4,*, Muhammad H. Tahir 5 , Farrukh Jamal 5 and Mohammed Elgarhy 6 Citation: Muhammad, M.; Bantan, R.A.R.; Liu, L.; Chesneau, C.; Tahir, M.H.; Jamal, F.; Elgarhy, M. A New Extended Cosine—G Distributions for Lifetime Studies. Mathematics 2021, 9, 2758. https://doi.org/10.3390/ math9212758
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