No Access

Bivariate Laplace Transform Order and Ordering of Reversed Residual Lives

S. Jayalekshmi

Department of Statistics, Cochin University of Science and Technology, Cochin 682 022, Kerala, India

E-mail Address: jayalekshmi1408@gmail.com

Search for more papers by this author

G. Rajesh

Department of Statistics, Cochin University of Science and Technology, Cochin 682 022, Kerala, India

E-mail Address: rajeshgstat@gmail.com

Corresponding author.

Search for more papers by this author

, and

N. Unnikrishnan Nair

Department of Statistics, Cochin University of Science and Technology, Cochin 682 022, Kerala, India

E-mail Address: unnikrishnannair4@gmail.com

Search for more papers by this author

https://doi.org/10.1142/S0218539322500061Cited by:0 (Source: Crossref)

Abstract

The Laplace transform order of reversed residual life, introduced by [I. Elbatal, The Laplace order and ordering of reversed residual life, Appl. Math. Sci.36 (2007) 1773–1788.] is used in the stochastic comparison of two life distributions. In this paper, we aim to study new notions of stochastic comparisons based on bivariate Laplace transform order of reversed residual lives. We investigate relationships the new stochastic order has with other existing bivariate orders. The interpretation of the new orders and their applications in different contexts are also pointed out.

Keywords:

References

1. T. Rolski and D. Stoyan, On the comparison of waiting times in GI/G/1 queues, Oper. Res. 24(1) (1976) 197–200. Crossref, Web of Science, Google Scholar
2. A. Alzaid, J. Soo Kim and F. Proschan, Laplace ordering and its applications, J. Appl. Probab. 28(1) (1991) 116–130. Crossref, Web of Science, Google Scholar
3. P. D. Thistle, Negative moments, risk aversion, and stochastic dominance, J. Financial Quant. Anal. 28(2) (1993) 301–311. Crossref, Web of Science, Google Scholar
4. M. Denuit, Laplace transform ordering of actuarial quantities, Insur.: Math. Econ. 29(1) (2001) 83–102. Crossref, Web of Science, Google Scholar
5. M. J. Goovaerts, R. Kaas, A. E. Van Heerwaarden and T. Bauwelinckx, Ordering of Actuarial Risks (Caire, Brussels, 1994). Google Scholar
6. F. Belzunce, E. Ortega and J. M. Ruiz, The Laplace order and ordering of residual lives, Stat. Probab. Lett. 42(2) (1999) 145–156. Crossref, Web of Science, Google Scholar
7. H. W. Block, T. H. Savits and H. Singh, The reversed hazard rate function, Probab. Eng. Inf. Sci. 12(1) (1998) 69–90. Crossref, Web of Science, Google Scholar
8. R. D. Gupta and A. K. Nanda, Some results on reversed hazard rate ordering, Commun. Stat. Theory Methods 30(11) (2001) 2447–2457. Crossref, Web of Science, Google Scholar
9. S. Bloch-Mercier, Monotone Markov processes with respect to the reversed hazard rate ordering: An application to reliability, J. Appl. Probab. 38(1) (2001) 195–208. Crossref, Web of Science, Google Scholar
10. K. Andersen Per, O. Borgan, R. D. Gill and N. Keiding, Statistical Models Based on Counting Processes (Springer Science and Business Media, 2012). Google Scholar
11. D. Sengupta, H. Singh and A. K. Nanda, The proportional reversed hazards model, Technical report, Applied Statistics Division (1998). Google Scholar
12. M. S. Finkelstein, On the reversed hazard rate, Reliab. Eng. Syst. Safety 78(1) (2002) 71–75. Crossref, Web of Science, Google Scholar
13. A. K. Nanda, H. Singh, N. Misra and P. Paul, Reliability properties of reversed residual lifetime, Commun. Stat. Theory Methods 32(10) (2003) 2031–2042. Crossref, Web of Science, Google Scholar
14. I. Elbatal, The Laplace order and ordering of reversed residual life, Appl. Math. Sci. 36 (2007) 1773–1788. Google Scholar
15. N. Gandotra, N. Gupta and R. K. Bajaj, Preservation properties of the Laplace transform and moment generating function ordering of residual life and inactivity time, J. Stat. Manag. Syst. 17(4) (2014) 301–310. Google Scholar
16. N. U. Nair and G. Asha, Some characterizations based on bivariate reversed mean residual life, ProbStat Forum 1 (2008). Google Scholar
17. A. Colangelo, Multivariate hazard orderings of discrete random vectors, Department of Economics, University of Insubria, 2005. Google Scholar
18. M. Shaked and J. G. Shanthikumar, Stochastic Orders (Springer Science and Business Media, 2007). Crossref, Google Scholar
19. G. Letac, J. Y. Tourneret and F. Chatelain, The bivariate gamma distribution with Laplace transform $(1 + a s + b t + c s t) - q :$ History, characterizations, estimation, (2007). Google Scholar
20. K. W. Gaede, Stochastic Orderings in Reliability, Lecture Notes-Monograph Series (1991), pp. 123–140. Google Scholar
21. G. Asha and N. Unnikrishnan Nair, Reliability properties of mean time to failure in age replacement models, Int. J. Reliab. Qual. Saf. Eng. 17(01) (2010) 15–26. Link, Google Scholar
22. M. Kayid, S. Izadkhah and S. Alshami, Laplace transform ordering of time to failure in age replacement models, J. Korean Stat. Soc. 45(1) (2016) 101–113. Crossref, Web of Science, Google Scholar
23. M. Izadi, M. Sharafi and B.-E. Khaledi, New nonparametric classes of distributions in terms of mean time to failure in age replacement, J. Appl. Probab. 55(4) (2018) 1238–1248. Crossref, Web of Science, Google Scholar
24. J. Corujo and J. E. Valds, Further results on stochastic orderings and aging classes in systems with age replacement, Probab. Eng. Inf. Sci. (2020) 1–30. Web of Science, Google Scholar