A new family of Marshall–Olkin extended generalized linear exponential distribution

The purpose of this paper is to introduce a new family of Marshall–Olkin extended generalized linear exponential distribution. This new family has the advantage of being capable of modeling various shapes of aging and failure criteria. The proposed family includes as special cases several Marshall–Olkin extended distributions studied in the literature such as exponential, Rayleigh, linear failure rate and Weibull, among others. Some statistical and reliability properties of the new family are discussed and an explicit expressions for the quantiles are derived. The method of the maximum likelihood estimation is used to estimate the unknown parameters. In addition, the asymptotic confidence intervals for the parameters are derived from the Fisher information matrix. Finally, the obtained results are validated using some real data sets and it is shown that the new family provides a better fit than some other known distributions.