Preservation of stochastic orders for random minima and maxima, with applications

Naval Research Logistics

Volumn 51, Issue 3, 2004, Pages 332-344

  Li, Xiaohu ^a   Zuo, Ming J ^b  

^a LANZHOU UNIVERSITY   (China)

^b UNIVERSITY OF ALBERTA   (Canada)

Author keywords

Aging properties; Increasing concave order; Increasing convex order; Lorenz order; Parallel system; Right spread order; Series system; Total time on test transform order

Indexed keywords

ECONOMICS; INTEGRAL EQUATIONS; PROBABILITY DENSITY FUNCTION; PROBABILITY DISTRIBUTIONS; RELIABILITY; THEOREM PROVING;

AGING PROPERTIES; INCREASING CONCAVE ORDER; INCREASING CONVEX ORDER; LORENZ ORDER; PARALLEL SYSTEM; PRESERVATION ORDERS; RANDOM MAXIMA; RANDOM MINIMA; RIGHT SPREAD ORDER; SERIES SYSTEM;

RANDOM PROCESSES;

EID: 1842559346     PISSN: 0894069X     EISSN: None     Source Type: Journal    
DOI: 10.1002/nav.10122     Document Type: Article

References (27)

1. A. Abouammoh and E. El-Neweihi, Closure of the NBUE and DMRL classes under formation of parallel systems, Statist Probab Lett 4 (1986), 223-225.
2. B.B. Arnold, Majorization and Lorenz order: A brief introduction, Springer-Verlag, New York, 1987.
3. R.E. Barlow and F. Proschan, Statistical theory of reliability and life testing, To Begin with, Silver Spring, Maryland, 1981.
4. J. Bartoszewicz, Applications of a general composition theorem to the star order of distributions, Statist Probab Lett 38 (1998), 1-9.
5. J. Bartoszewicz, Stochastic comparisons of random minima and maxima from life distributions, Statist Probab Lett 55 (2001), 107-112.
6. F. Belzunge, On a characterization of right sprerad order by the increasing convex order, Statist Probab Lett 45 (1999), 103-110.
7. F. Belzunce, J. Candel, and J.M. Ruiz, Dispersive orderings and characterization of ageing classes, Statist Probab Lett 28 (1996), 321-327.
8. J. Cao and Y. Wang, Correction for 'The NBUC and NWUC classes of life distributions,' J Appl Probab 29 (1992), 753.
9. J. Cao and Y. Wang, The NBUC and NWUC classes of life distributions, J Appl Probab 28 (1991), 473-479.
10. J.V. Deshpande, S.C. Kochar, and H. Singh, Aspects of positive ageing, J Appl Probab 23 (1986), 748-758.
11. E. Fagiuoly, F. Pellerey, and M. Shaked, A characterization of the dilation order and its applications, Statist Papers 40 (1999), 393-406.
12. J.M. Fernandez-Ponce, S.C. Kochar, and J. Muñoz-Pérez, Partial orderings of distributions based upon right spread function. J Appl Probab 35 (1998), 221-228.
13. M. Franco, J.M. Ruiz and M.C. Ruiz, On closure of the IFR(2) and NBU(2) classes, J Appl Probab 38 (2001), 236-242.
14. D.L. Grosh, A parallel system of IFR units is IFR, IEEE Trans Reliability 31 (1982), 403.
15. M.I. Hends, A.F. Mashhour, and M.A. Montasser, Closurer of the NBud class of life distribution under formation of Parallel system, J Appl Probab 30 (1993), 925-978.
16. I. Jewitt, Choosing between risky prospects: The characterization of comparative static results, and location independent risk, Management Sci 35 (1989), 60-70.
17. B. Klefsjö, TTT-plotting - a tool for both theoretical and practical problems, J Statist Plann Inference 29 (1991), 111-124.
18. S.C. Kochar and K.C. Carriére, Connections among various variability orderings, Statist Probab Lett 35 (1997), 327-333.
19. S.C. Kochar, X. Li, and M. Shaked, The total time on test transform and the excess wealth stochastic order of distributions, Adv Appl Probab 34 (2002), 826-845.
20. S.C. Kochar and D.P. Wiens, Partial ordering of life distributions with respect to their aging properties, Naval Res Logist Quart 34 (1987), 823-829.
21. X. Li and J. Lu, Stochastic comparisons on residual life and inactivity time of series and parallel systems, Probab Engrg Inform Sci 17 (2003), 267-276.
22. X. Li and S.C. Kochar, Some new results involving the NBU(2) classes of life distributions, J Appl Probab 38 (2001), 242-247.
23. A. Müller and D. Stoyan, Comparison methods for stochastic models and risks, Wiley, New York, 2002.
24. M. Shaked and J.G. Shanthikumar, Stochastic orders and their applications, Academic Press, San Diego, 1994.
25. M. Shaked and J.G. Shanthikumar, Two variability orders, Probab Engrg Inform Sci 12 (1998), 1-23.
26. M. Shaked and T. Wong, Stochastic comparisons of random minima and maxima, J Appl Probab 34 (1997), 420-425.
27. M. Shaked, On the distribution of the minimum and of the maximum of a random number of i.i.d. random variables. In: G.P. Patil, S. Kotz and J. Ord (Editors), Statistical Distribution in Scientific Work, vol. 1. Reidel, Dordrecht, (1975), 363-380.