Abstract
The purpose of this paper is to introduce, discuss and analyze a new family of Marshall–Olkin extended distributions. This new family generalizes the following Marshall–Olkin extended distributions: (i) exponential, (ii) Rayleigh, (iii) linear failure rate, and (iv) Weibull. Some statistical and reliability properties of the new family are discussed. The maximum likelihood estimates of its unknown parameters are obtained. The obtained results are validated using a real data set and it is shown that the new family provides a better fit than some other known distributions.