Inference on the Stress-Strength Model from Weibull Gamma Distribution

Authors

Mohamed A. W. Mahmoud, Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City (11884), Cairo, EgyptFollow
Rashad M. EL-Sagheer, Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City (11884), Cairo, EgyptFollow
Mahmoud M. M. Mansour, Department of Basic Science, Faculty of Engineering, The British University in Egypt, El Sherouk City, Cairo, EgyptFollow

Author Country (or Countries)

Egypt

Abstract

The point at issue of this paper is to deliberate point and interval estimations of the stress - strength function, R. The maximum likelihood, Bayes, and parametric bootstrap estimators are obtained as point estimations of R. Based on the maximum likelihood estimate (MLE) of R, the distribution of R is determined and hence its confidence interval (CI) is estimated. The variance of ˆ R has been got in a closed form. Furthermore, four bootstrap CIs of R have been obtained. The results of Bayes estimation are computed under the squared error loss (SEL) and the LINEX loss functions. The acceptance rejection principle algorithm is applied to obtain the credible CI of R. Finally, two explanatory examples are introduced to explicate the precision of the obtained estimators .

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/110313

Recommended Citation

A. W. Mahmoud, Mohamed; M. EL-Sagheer, Rashad; and M. M. Mansour, Mahmoud (2017) "Inference on the Stress-Strength Model from Weibull Gamma Distribution," Applied Mathematics & Information Sciences: Vol. 11: Iss. 3, Article 13.
DOI: http://dx.doi.org/10.18576/amis/110313
Available at: https://digitalcommons.aaru.edu.jo/amis/vol11/iss3/13