Ordering results of extreme order statistics from heterogeneous Gompertz-Makeham random variables

Gompertz-Makeham distribution, which is not a member of the location-scale family, has been widely used for describing human mortality, determining policies in insurance, establishing actuarial tables and growth models. In this paper, we study stochastic comparisons for extreme order statistics from independent heterogeneous Gompertz-Makeham samples. The comparisons are carried out in the sense of usual stochastic, hazard rate, reversed hazard rate and likelihood ratio orderings. The effects of the changes in the parameters based on vector majorization and multivariate chain majorization with heterogeneity in two and three parameters have been investigated.