Stochastic orders of the Marshall–Olkin extended distribution

A general method of introducing a parameter, called tilt parameter, has been discussed by Marshall and Olkin (1997) to give more flexibility in modelling. In this paper, we take the tilt parameter of the Marshall–Olkin extended family as a random variable. The closure of this model under different stochastic orders viz. ageing intensity order, likelihood ratio order, shifted likelihood ratio orders and shifted hazard rate orders is discussed.