Dispersive functions and stochastic orders

• Autorzy: Jarosław Bartoszewicz
• Języki publikacji: EN

Abstrakty

EN

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

Słowa kluczowe

EN

stationary renewal distribution; mean residual life; preservation theorem; partial orders; hazard function; dispersive function

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 1996-1997
• Tom: 24
• Numer: 4
• Strony: 429-444

Daty

wydano

1997

otrzymano

1996-10-04

Twórcy

autor

Jarosław Bartoszewicz

• Mathematical Institute, University of Wrocław, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

Bibliografia

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