Results on Relative Mean Residual Life and Relative Cumulative Residual Entropy

  • Vali Zardasht University of Mohaghegh Ardabili
DOI: https://doi.org/10.19139/soic.v7i1.384
Keywords: Ageing class, Cumulative residual entropy, Residual lifetime, Relative ageing, Reliability measures, Partial ordering.

Abstract

Wei [21] has proposed the relative mean residual life function for comparing two lifetime distributions and studied its properties and relationship with other stochastic orders. In this paper, we obtain some new results on the relative mean residual life function and give a characterization result for a relative ordering based on this function. Motivated by this notion, we also introduce two notions of the dynamic relative cumulative residual entropy functions. Their properties and relationship with other relative orderings are investigated.

References

M. Asadi, and Y. Zohrevand, On the dynamic cumulative residual entropy, Journal of Statistical Planning and Inference, vol. 137,pp. 1931-1941, 2007.

R. Barlow, and F. Proschan, Statistical Theory of Reliability and Life Testing, Probability Models, Holt, Rinehart and Winston,New-York, 1975.

D. R. Cox, Regression models and life-tables (with discussion), Journal of the Royal Statistical Society, Series B, vol. 34, pp.187–208, 1972.

J. V. Deshpande, S. C. Kochar and H. Singh, Aspects of positive ageing, Journal of Applied Probability, vol. 23, pp. 748-?58, 1986.

A., Di Crescenzo and M. Longobardi, On cumulative entropies, Journal of Statistical Planning and Inference, vol. 139, pp. 4072–4087, 2009.

M. Finkelstein, On relative ordering of mean residual lifetime functions, Statistics and Probability Letters, vol. 76, pp. 939–944, 2006.

R. C. Gupta, Role of equilibrium distribution in reliability studies, Probability in the Engineering and Informational Sciences, vol.21, pp. 315-334, 2007.

N. K. Hazra and A. K. Nanda, On some generalized orderings: In the spirit of relative ageing, Communications in Statistics -Theory and Methods, vol. 45, no. 20, pp. 6165–6181, 2016.

V. Kalashnikov and S. T. Rachev, Characterization of queueing models and their stability, in Probability Theory and Mathematical Statistics, Prohorov et al., ed. , vol. 2, pp. 37–53, 1986.

M. Kayid, S. Izadkhah and M. J. Zuo, Some results on the relative ordering of two frailty models, Statistical Papers, pp. 1–15, 2015.

C. Lai and M. Xie, Stochastic Ageing and Dependence for Reliability, Springer, New York, 2006.

C. Li and X. Li, Relative ageing of series and parallel systems with statistically independent and heterogeneous component lifetimes,IEEE, Transaction on Reliability, vol. 65, no. 2, pp. 1014-1021, 2016.

N. Misra, J. Francis and S. Naqvi, Some sufficient conditions for relative aging of life distributions, Probability in the Engineering and Informational Sciences, vol. 31, pp. 83-99, 2017.

J. Navarro, Y. del Aguila and M. Asadi, Some new results on the cumulative residual entropy, Journal of Statistical Planning and Inference, vol. 140, pp. 310–322, 2010.

M. Rao, More on a new concept of entropy and information, Journal of Theoretical Probability, vol. 18, pp. 967-981, 2005.

M. Rao, Y. Chen, B. C. Vemuri and F. Wang, Cumulative residual entropy: a new measure of information, IEEE Transactions on Information Theory, vol. 50, pp. 1220-1228, 2004.

S. I. Resnick, A Probability Path, Birkhauser, Boston, 1999.

D. Sengupta and J. V. Deshpande, Some results on the relative ageing of two life distributions, Journal of Applied Probability, vol.31, pp. 991-1003, 1994.

M. Shaked and J. G. Shanthikumar, Stochastic orders, Springer, New York, 2007.

C. E. Shannon, A mathematical theory of communication, Bell System Technology Journal, vol. 27, pp. 279-423, 1948.

X. Wei, Relative mean residual life: Theorey and related topics, Microelectronics Relaibility, vol. 32 no. 9, pp. 1319–1326, 1992.

Published
2019-01-07
How to Cite
Zardasht, V. (2019). Results on Relative Mean Residual Life and Relative Cumulative Residual Entropy. Statistics, Optimization & Information Computing, 7(1), 150-159. https://doi.org/10.19139/soic.v7i1.384
Issue
Vol 7 No 1 (2019)
Section
Research Articles
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