Preservation of classes of life distributions and stochastic orders under weighting

Statistics and Probability Letters

Volumn 76, Issue 6, 2006, Pages 587-596

  Bartoszewicz, Jarosław ^a   Skolimowska, Magdalena ^a  

^a UNIVERSITY OF WROC AW   (Poland)

Author keywords

DFR; DFRA; DRFR; Hazard rate; IFR; IFRA; IRFR; Length biased distributions; Lorenz curve; NBU; NWU; Partial orders; Reversed hazard rate; Weighted distributions

Indexed keywords

EID: 33344468593     PISSN: 01677152     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.spl.2005.09.003     Document Type: Article

References (25)

1. V. Aggarwal R. Singh On optimum stratification with proportional allocation for a class of Pareto distributions Comm. Statist. Theory Methods 13 1984 3107-3116
2. Arnold, B.C., 1987. Majorization and the Lorenz Order: A Brief Introduction. Lectures Notes in Statistics, vol. 43. Springer, Berlin.
3. I. Bagai S.C. Kochar On tail ordering and comparison of failure rates Comm. Statist. Theory Methods 15 1986 1377-1388
4. J. Bartoszewicz Dispersive ordering and monotone failure rate distributions Adv. Appl. Probab. 17 1985 472-474
5. J. Bartoszewicz Dispersive functions and stochastic orders Appl. Math. (Warsaw) 24 1997 429-444
6. J. Bartoszewicz Mixtures of exponential distributions and stochastic orders Statist. Probab. Lett. 57 2002 23-31
7. Bartoszewicz, J., Skolimowska, M., 2004a. Preservation of classes of life distributions under weighting. Mathematical Institute University of Wrocław, Report No. 142, available at www.math.uni.wroc.pl/ mathbank/preprint/
8. Bartoszewicz, J., Skolimowska, M., 2004b. Stochastic ordering of weighted distributions. Mathematical Institute University of Wrocław, Report No. 143, available at www.math.uni.wroc.pl/mathbank/preprint/
9. F. Belzunce R.E. Lillo J.M. Ruiz M. Shaked Stochastic comparisons of nonhomogeneous processes Probab. Eng. Inform. Sci. 15 2001 199-224
10. M. Brown F. Proschan Imperfect repair J. Appl. Probab. 20 1983 851-859
11. D.R. Cox The Renewal Theory 1962 Methuen London
12. A. Di Crescenzo Some results on the proportional reversed hazards model Statist. Probab. Lett. 50 2000 313-321
13. R.C. Gupta J.P. Keating Relations for reliability measures under length biased sampling Scand. J. Statist. 13 1986 49-56
14. R.C. Gupta R.D. Gupta P.L. Gupta Modelling failure time data by Lehmann alternatives Comm. Statist. Theory Methods 27 1998 887-904
15. K. Jain H. Singh I. Bagai Relations for reliability measures of weighted distributions Comm. Statist. Theory Methods 18 1989 4393-4412
16. K. Joag-dev S. Kochar F. Proschan A general composition theorem and its applications to certain partial orderings of distributions Statist. Probab. Lett. 22 1995 111-119
17. S. Karlin Total Positivity 1968 Stanford University Press Stanford
18. A.W. Marshall I. Olkin Inequalities: Theory of Majorization and its Applications 1979 Academic Press New York
19. Marshall, A.W., Proschan, F., 1972. Convexity preserving scale transformations. In: Proceedings of the Third Symposium on Inequalities, Los Angeles, September 1-9, 1969, Academic Press, New York, pp. 225-234.
20. A.K. Nanda K. Jain Some weighted distribution results on univariate and bivariate cases J. Statist. Plann. Inference 77 1999 169-180
21. Parzen, E., 1980. Quantile functions, convergence in quantile, and extreme value distribution theory. Technical Report B-3, Statistical Institute, Texas A&M University College Station, Texas.
22. G.P. Patil C.R. Rao The weighted distributions: A survey and their applications P.R. Krishnaiah Applications of Statistics 1977 North-Holland Amsterdam 385-405
23. C.R. Rao Weighted distributions arising out of methods of ascertainment: what population does a sample represent A.C. Atkinson S.E. Fienberg A Celebration of Statistics: The ISI Centenary Volume 1985 Springer New York 543-569
24. S.M. Ross The inspection paradox Probab. Eng. Inform. Sci. 17 2003 47-51
25. M. Shaked J.G. Shanthikumar Stochastic Orders and their Applications 1994 Academic Press New York