On Inference about Tilt Parameter in Marshall-Olkin Family of Distributions

Marshall and Olkin [Biometrika 84, 641–652, 1997] introduced a method for constructing a new distribution by adding a new parameter, called tilt parameter, to a parent distribution. It is observed that adding this parameter leads to a more flexible model than the parent model. In this paper, different estimators for tilt parameter as a major parameter are presented. Their performances are compared using Monte Carlo simulations. Hypothesis testing and interval estimation of tilt parameter using Rao score test is discussed.