Stochastic Comparisons of General Proportional Mean Past Lifetime Frailty Model

Fatemeh Hooti (), Jafar Ahmadi () and N. Balakrishnan ()
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Fatemeh Hooti: Ferdowsi University of Mashhad
Jafar Ahmadi: Ferdowsi University of Mashhad
N. Balakrishnan: McMaster University

Sankhya A: The Indian Journal of Statistics, 2022, vol. 84, issue 2, No 17, 844-866

Abstract: Abstract In this paper, the general proportional mean past lifetime frailty model is considered, from which the unconditional cumulative distribution and density functions of the lifetime variable are derived. Dependency between the two variables are studied. Stochastic comparisons are made through which it is shown that some well-known stochastic orderings between two frailty variables carry over to the corresponding lifetime variables. The effects of baseline variable and the frailty variable on the proposed frailty model are studied. The relative mean past lifetime ordering is introduced and some relative ordering between two lifetime random variables with different frailty variables are studied. Also a simulation study is given to illustrate some results.

Keywords: Frailty model; PMPL model; Reversed hazard rate ordering; Likelihood ratio ordering; Stochastic ordering; Relative ordering; Totally positive of order 2; Reverse regular of order 2; 62N05; 60E15 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s13171-020-00222-3

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