Modified Generalized Linear Exponential Distribution: Properties and applications

Abstract

In this paper, we propose a new four-parameter lifetime distribution called modified generalized linear exponential distribution. The proposed distribution is a modification of the generalized linear exponential distribution. Several important lifetime distributions in reliability engineering and survival analysis are considered as special sub-models including modified Weibull, Weibull, linear exponential and generalized linear exponential distributions, among others. We study the mathematical and statistical properties of the proposed distribution including moments, moment generating function, modes, and quantile. We then examine hazard rate, mean residual life, and variance residual life functions of the distribution. A significant property of the new distribution is that it can have a bathtub-shaped, which is very flexible for modeling reliability data.The four unknown parameters of the proposed model are estimated by the maximum likelihood. Finally, two practical real data sets are applied to show that the proposed distribution provides a superior fit than the other sub-models and some well-known distributions.