On the Comparison of Reliability Experiments Based on the Convolution Order

Journal of the American Statistical Association

Volumn 98, Issue 463, 2003, Pages 693-702

  Shaked, Moshe ^a   Suarez Llorens, Alfonso ^b  

^a University of Arizona   (United States)

^b UNIVERSITY OF CÁDIZ   (Spain)

Author keywords

Coherent systems; Convolution order; Coxian distributions; Dispersive order; Information comparisons; Order statistics; Poles and zeros of rational functions; Signatures; Stochastic orders

Indexed keywords

EID: 0242510859     PISSN: 01621459     EISSN: None     Source Type: Journal    
DOI: 10.1198/016214503000000602     Document Type: Article

References (32)

1. Asmussen, S. (1987), Applied Probability and Queues, New York: Wiley.
2. Blackwell, D. (1951), "Comparison of Experiments," in Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, Berkeley, CA: University of California Press, pp. 93-102.
3. _ (1953), "Equivalent Comparison of Experiments," Annals of Mathematical Statistics, 24, 265-272.
4. Boland, P. J., Hu, T., Shaked, M., and Shanthikumar, J. G. (2002), "Stochastic Ordering of Order Statistics II," in Modeling Uncertainly: An Examination of Stochastic Theory, Methods, and Applications, eds. M. Dror, P. L'Ecuyer, and F. Szidarovszky, Boston: Kluwer, pp. 607-623.
5. Eaton, M. L. (1992), "A Group Action on Covariances With Applications to the Comparison of Linear Normal Experiments," in Stochastic Inequalities, eds. M. Snaked and Y. L. Tong, Hayward, CA: Institute of Mathematical Statistics, pp. 76-90.
6. Esary, J. D., and Marshall, A. W. (1970), "Coherent Life Functions," SIAM Journal on Applied Mathematics, 18, 810-814.
7. Goel, P. K. (1988), "Comparison of Experiments and Information in Censored Data," in Statistical Decision Theory and Related Topics VI, Vol. 2, eds. S. S. Gupta and J. O. Berger, New York: Springer-Verlag, pp. 335-349.
8. Goel, P. K., and DeGroot, M. H. (1979), "Comparison of Experiments and Information Measures," The Annals of Statistics, 7, 1066-1077.
9. Greenshtein, E., and Torgersen, E. (1997), "Statistical Information and Expected Number of Observations for Sequential Experiments," Journal of Statistical Planning and Inference, 59, 229-240.
10. Hansen, O. H., and Torgersen, E. N. (1974), "Comparison of Linear Experiments," The Annals of Statistics, 2, 367-373.
11. Hauke, J., and Markiewicz, A. (1994), "Comparison of Experiments via a Group Majorization Ordering," Metrika, 41, 201-209.
12. Hollander, M., Proschan, F., and Sconing, J. (1987), "Measuring Information in Right-Censored Models," Naval Research Logistics, 34, 669-681.
13. Khaledi, B.-E., and Kochar, S. (2000), "On Dispersive Ordering Between Order Statistics in One-Sample and Two-Sample Problems," Statistics and Probability Letters, 46, 257-261.
14. Kochar, S. C., Mukerjee, H., and Samaniego, F. J. (1999), "The 'Signature' of a Coherent System and Its Application to Comparisons Among Systems," Naval Research Logistics, 46, 507-523.
15. Lehmann, E. L. (1959), Testing Statistical Hypotheses, New York: Wiley.
16. _ (1988), "Comparing Location Experiments," The Annals of Statistics, 16, 521-533.
17. Lillo, R. E., Nanda, A. K., and Shaked, M. (2001), "Preservation of Some Likelihood Ratio Stochastic Orders by Order Statistics," Statistics and Probability Letters, 51, 111-119.
18. Nanda, A. K., and Shaked, M. (2001), "The Hazard Rate and the Reversed Hazard Rate Orders, With Applications to Order Statistics," Annals of the Institute of Statistical Mathematics, 53, 853-864.
19. Samaniego, F. J. (1985), "On the Closure of the IFR Class Under Formation of Coherent Systems," IEEE Transactions on Reliability, R-34, 69-72.
20. Shaked, M., and Shanthikumar, J. G. (1994), Stochastic Orders and Their Applications, Boston: Academic Press.
21. Shaked, M., and Tong, Y. L. (1990), "Comparison of Experiments for a Class of Positively Dependent Random Variables," Canadian Journal of Statistics, 18, 79-86.
22. Shaked, M., and Wong, T. (1997), "Stochastic Orders Based on Ratios of Laplace Transforms," Journal of Applied Probability. 34, 341-348.
23. Stepniak, C. (1994), "A Note on Comparison of Genetic Experiments," The Annals of Statistics, 22, 1630-1632.
24. _ (1997a), "Matrix Loss in Comparison of Linear Experiments," Linear Algebra and Its Applications, 264, 358-365.
25. _ (1997b), "Sandwich Theorem in Comparison of Multivariate Normal Experiments," Statistics and Probability Letters, 33, 281-284.
26. _ (1997c), "Comparison of Normal Linear Experiments by Quadratic Forms," Annals of the Institute of Statistical Mathematics, 49, 569-584.
27. Sumita, U., and Masuda, Y. (1987), "Classes of Probability Density Functions Having Laplace Transform With Negative Zeros and Poles," Advances in Applied Probability, 19, 632-651.
28. Takano, K. (1951), "Certain Fourier Transforms of Distributions," Tôhoku Mathematical Journal, 2, 306-315.
29. Torgersen, E. N. (1984), "Orderings of Linear Models," Journal of Statistical Planning and Inference, 9, 1-17.
30. _ (1991), Comparison of Statistical Experiments, Cambridge, U.K.: Cambridge University Press.
31. _ (1994), "Information Ordering and Stochastic Ordering," in Stochastic Orders and Their Applications, eds, M. Snaked and J. G. Shanthikumar, Boston: Academic Press, pp. 275-319.
32. Zemanian, A. H. (1959), "On the Pole and Zero Location of Rational Laplace Transforms of Non-Negative Functions," Proceedings of the American Mathematical Society, 10, 868-872.