Title: Ordering Results for Order Statistics from Two Heterogeneous Marshall-Olkin Generalized Exponential Distributions

Author(s): Abedin Haidari, Ghobad Barmalzan and Narayanaswamy Balakrishnan
Issue: Volume 80 Series B Part 2 Year 2018
Pages: 292 -- 304
Adding parameters to a known distribution is a useful way of constructing flexible families of distributions. Marshall and Olkin (Biometrika, 84, 641– 652, 1997) introduced a general method of adding a shape parameter to a family of distributions. In this paper, based on the Marshall-Olkin extension of a specified distribution, we introduce a new models referred to as Marshal- Olkin generalized exponential (MOGE) models, which include as a special case the well-known generalized exponential distribution. Next, we establish some stochastic comparisons between the corresponding order statistics based on majorization, weak majorization and p-larger theory. The results established here extend some well-known results in the literature about the generalized exponential distribution.
AMS (2000) subject classification. Primary: 60E15; Secondary: 90B25.
Keywords and phrases: Weak majorization order, P-larger order, Order statistics, Usual stochastic order, Marshall-Olkin generalized exponential model