Some results on discrete mixture failure rates

Abstract

Some properties of the discrete mixture failure rates are studied. Specifically, similar to the continuous case, it is shown that the population mixture failure rate is always smaller than the unconditional expectation in the family of subpopulations failure rates. The analog of the multiplicative and the additive frailty models is introduced via the corresponding survival function. Another approach via the alternative discrete failure rate is also discussed. Stochastic comparisons for two mixed distributions with equal and different mixing distributions are studied.

Keywords:

• Discrete mixture failure rate
• multiplicative and additive frailty models
• partial stochastic order
• stochastic order of lifetimes

Acknowledgements

The authors would like to thank the reviewer for helpful comments and valuable suggestions.

Additional information

Funding

The work of the first author was 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 first author was also supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2016R1A2B2014211). The work of the second author was supported by the National Research Foundation (NRF) of South Africa, grant IFR2011040500026.