# On some mortality rate processes and mortality deceleration with age

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## Abstract

A specific mortality rate process governed by the non-homogeneous Poisson process of point events is considered and its properties are studied. This process can describe the damage accumulation in organisms experiencing external shocks and define its survival characteristics. It is shown that, although the sample paths of the unconditional mortality rate process are monotonically increasing, the population mortality rate can decrease with age and, under certain assumptions, even tend to zero. The corresponding analysis is the main objective of this paper and it is performed using the derived conditional distributions of relevant random parameters. Several meaningful examples are presented and discussed.

## Keywords

Gompertz law of mortality Fixed heterogeneity Evolving heterogeneity Nonhomogeneous Poisson process Mortality rate Mortality process## Mathematics Subject Classification

62P10 (Applications to biology and medical sciences) 62N05 (Reliability and life testing)## Notes

### Acknowledgments

The authors would like to thank the Editor and the referees for helpful comments and suggestions, which have improved the presentation of this paper. The work of the first author was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (No. 2011-0017338). The work of the first author was also supported by Priority Research Centers Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2009-0093827). The work of the second author was supported by the NRF (National Research Foundation of South Africa) grant IFR2011040500026.

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