2019/12/06 by Amarjit Kundu, Shovan Chowdhury, Kundu, Amarjit +3
Mathematics · Social Sciences · #Applications (stat.AP) #FOS: Computer and information sciences #Insurance, Mortality, Demography, Risk Management #Statistical Distribution Estimation and Applications
paper · pdf · doi:10.48550/arxiv.1912.04171
openalex publication_date 2019/12/06 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
The Gompertz-Makeham distribution, which is used commonly to represent\nlifetimes based on laws of mortality, is one of the most popular choices for\nmortality modelling in the field of actuarial science. This paper investigates\nordering properties of the smallest and largest lifetimes arising from two sets\nof heterogeneous groups of insurees following respective Gompertz-Makeham\ndistributions. Some sufficient conditions are provided in the sense of usual\nstochastic ordering to compare the smallest and largest lifetimes from two sets\nof dependent variables. Comparison results on the smallest lifetimes in the\nsense of hazard rate ordering and ageing faster ordering are established for\ntwo groups of heterogeneous independent lifetimes. Under similar set-up, no\nreversed hazard rate ordering is shown to exist between the largest lifetimes\nwith the use of a counter-example. Finally, we present sufficient conditions to\nstochastically compare two sets of independent heterogeneous lifetimes under\nrandom shocks by means of usual stochastic ordering. Such comparisons for the\nsmallest lifetimes are also carried out in terms of hazard rate ordering.\n