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Stochastic Comparisons of General Proportional Mean Past Lifetime Frailty Model

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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.

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Acknowledgements

The authors would like to thank the Editor and the anonymous reviewer for their comments and suggestions to improve the quality of the paper.

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Authors and Affiliations

  1. Department of Statistics, Ferdowsi University of Mashhad, P. O. Box 1159, Mashhad, 91775, Iran

    Fatemeh Hooti & Jafar Ahmadi

  2. Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario L8S 4K1, Canada

    N. Balakrishnan

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  1. Fatemeh Hooti
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  2. Jafar Ahmadi
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  3. N. Balakrishnan
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Correspondence to Jafar Ahmadi.

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Hooti, F., Ahmadi, J. & Balakrishnan, N. Stochastic Comparisons of General Proportional Mean Past Lifetime Frailty Model. Sankhya A 84, 844–866 (2022). https://doi.org/10.1007/s13171-020-00222-3

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