Weibull-Linear Exponential Distribution and Its Applications

Authors

Ahmed. G. Atia, Mathematics Department, Faculty of Science, Mansoura University,Mansoura 35516, EgyptFollow
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, Egypt\\ High Institute of Computer and Management Information System, First Statement, New Cairo 11865, Cairo, EgyptFollow
Beih. S. El-Desouky, Mathematics Department, Faculty of Science, Mansoura University,Mansoura 35516, EgyptFollow

Abstract

In this article, a new four-parameter lifetime distribution, namely, the Weibull-Linear exponential distribution is defined and studied. Several of its structural properties such as quartiles, moments, mean waiting time, mean residual lifetime, Renyi entropy, mode, and order statistics are derived. Based on the idea of the Weibull T − X family, the new density function of this model is developed. The model parameters, as well as some of the lifetime parameters (reliability and failure rate functions), are estimated using the maximum likelihood method. Asymptotic confidence intervals estimates of the model parameters are also evaluated by using the Fisher information matrix. Moreover, to construct the asymptotic confidence intervals of the reliability and failure rate functions, we need to find their variance of them, which are approximated by the delta method. A real data set is used to illustrate the application of the Weibull-Linear Exponential distribution.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/jsap/120114

Recommended Citation

G. Atia, Ahmed.; A. W. Mahmoud, Mohamed.; M. EL-Sagheer, Rashad.; and S. El-Desouky, Beih. (2023) "Weibull-Linear Exponential Distribution and Its Applications," Journal of Statistics Applications & Probability: Vol. 12: Iss. 1, Article 14.
DOI: http://dx.doi.org/10.18576/jsap/120114
Available at: https://digitalcommons.aaru.edu.jo/jsap/vol12/iss1/14