Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ordering properties of the smallest and largest lifetimes in
  Gompertz-Makeham model   The Gompertz-Makeham distribution, which is used commonly to represent
lifetimes based on laws of mortality, is one of the most popular choices for
mortality modelling in the field of actuarial science. This paper investigates
ordering properties of the smallest and largest lifetimes arising from two sets
of heterogeneous groups of insurees following respective Gompertz-Makeham
distributions. Some sufficient conditions are provided in the sense of usual
stochastic ordering to compare the smallest and largest lifetimes from two sets
of dependent variables. Comparison results on the smallest lifetimes in the
sense of hazard rate ordering and ageing faster ordering are established for
two groups of heterogeneous independent lifetimes. Under similar set-up, no
reversed hazard rate ordering is shown to exist between the largest lifetimes
with the use of a counter-example. Finally, we present sufficient conditions to
stochastically compare two sets of independent heterogeneous lifetimes under
random shocks by means of usual stochastic ordering. Such comparisons for the
smallest lifetimes are also carried out in terms of hazard rate ordering.

21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom