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.