Dispersive functions and stochastic orders

Jarosław Bartoszewicz

Applicationes Mathematicae (1997)

  • Volume: 24, Issue: 4, page 429-444
  • ISSN: 1233-7234

Abstract

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Generalizations of the hazard functions are proposed and general hazard rate orders are introduced. Some stochastic orders are defined as general ones. A unified derivation of relations between the dispersive order and some other orders of distributions is presented

How to cite

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Bartoszewicz, Jarosław. "Dispersive functions and stochastic orders." Applicationes Mathematicae 24.4 (1997): 429-444. <http://eudml.org/doc/219183>.

@article{Bartoszewicz1997,
abstract = {Generalizations of the hazard functions are proposed and general hazard rate orders are introduced. Some stochastic orders are defined as general ones. A unified derivation of relations between the dispersive order and some other orders of distributions is presented},
author = {Bartoszewicz, Jarosław},
journal = {Applicationes Mathematicae},
keywords = {stationary renewal distribution; mean residual life; preservation theorem; partial orders; hazard function; dispersive function; hazard functions; stochastic orders; hazard rate orders},
language = {eng},
number = {4},
pages = {429-444},
title = {Dispersive functions and stochastic orders},
url = {http://eudml.org/doc/219183},
volume = {24},
year = {1997},
}

TY - JOUR
AU - Bartoszewicz, Jarosław
TI - Dispersive functions and stochastic orders
JO - Applicationes Mathematicae
PY - 1997
VL - 24
IS - 4
SP - 429
EP - 444
AB - Generalizations of the hazard functions are proposed and general hazard rate orders are introduced. Some stochastic orders are defined as general ones. A unified derivation of relations between the dispersive order and some other orders of distributions is presented
LA - eng
KW - stationary renewal distribution; mean residual life; preservation theorem; partial orders; hazard function; dispersive function; hazard functions; stochastic orders; hazard rate orders
UR - http://eudml.org/doc/219183
ER -

References

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  1. A. N. Ahmed, A. Alzaid, J. Bartoszewicz and S. C. Kochar (1986), Dispersive and superadditive ordering, Adv. in Appl. Probab. 18, 1019-1022. Zbl0611.60018
  2. A. A. Alzaid and F. Proschan (1992) Dispersivity and stochastic majorization, Statist. Probab. Lett. 13, 275-278. Zbl0744.62073
  3. R. E. Barlow, D. J. Bartholomew, J. M. Bremner and H. D. Brunk (1972), Statistical Inference under Order Restrictions, Wiley, New York. Zbl0246.62038
  4. R. E. Barlow and F. Proschan (1975), The Statistical Theory of Reliability, Holt, Rinehart and Winston, New York. Zbl0379.62080
  5. J. Bartoszewicz (1985), Moment inequalities for order statistics from ordered families of distributions, Metrika 32, 383-389. Zbl0584.62030
  6. J. Bartoszewicz (1987), A note on dispersive ordering defined by hazard functions, Statist. Probab. Lett. 6, 13-16. Zbl0633.62017
  7. N. B. Ebrahimi and H. Zahedi (1992), Memory ordering of survival functions, Statistics 23, 337-345. Zbl0811.62021
  8. M. Hollander and F. Proschan (1984), Nonparametric concepts and methods in reliability, in: Handbook of Statistics, Elsevier, New York, Vol. 4, Zbl0596.62099
  9. 613-655. 
  10. J. Keilson and U. Sumita (1982), Uniform stochastic ordering and related inequalities, Canad. J. Statist. 10, 181-189. Zbl0516.60063
  11. J. Lynch, G. Mimmack and F. Proschan (1987), Uniform stochastic orderings and total positivity, ibid. 15, 63-69. Zbl0617.62005
  12. Y. Sathe (1984), A comment on star ordering and tail ordering, Adv. in Appl. Probab. 16, 692. Zbl0542.60018
  13. M. Shaked (1982), Dispersive ordering of distributions, J. Appl. Probab. 19, 310-320. Zbl0481.60022
  14. M. Shaked and J. G. Shanthikumar (1994), Stochastic Orders and Their Applications, Academic Press, New York. Zbl0806.62009
  15. W. R. van Zwet (1964), Convex Transformations of Random Variables, Mathematisch Centrum, Amsterdam. Zbl0125.37102

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