Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-05T08:56:27.582Z Has data issue: false hasContentIssue false
  • English
  • Français

Partial Orderings of Distributions Based on Right-Spread Functions

Part of: Distribution theory Survival analysis and censored data

Published online by Cambridge University Press:  14 July 2016

J. M. Fernandez-Ponce ,
S. C. Kochar  and
J. Muñoz-Perez
J. M. Fernandez-Ponce*
Affiliation:
Universidad de Sevilla
S. C. Kochar*
Affiliation:
Indian Statistical Institute
J. Muñoz-Perez*
Affiliation:
Universidad de Málaga
*
∗Postal address: Dpto. Estadística e Investigación Operativa, Facultad de Matemáticas, Universidad de Sevilla, Avda. Reina Mercedes, s/n, 41012-Sevilla, Spain.
∗∗Postal address: Indian Statistical Institute, 7, SJS Sansanwal Marg, New Delhi-110016, India.
∗∗∗Postal address: Escuela Superior de Ingenieria Informática, Facultad de, Universidad de Málaga, Campo de Teatinos, 29071-Malaga, Spain.
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper we introduce a quantile dispersion measure. We use it to characterize different classes of ageing distributions. Based on the quantile dispersion measure, we propose a new partial ordering for comparing the spread or dispersion in two probability distributions. This new partial ordering is weaker than the well known dispersive ordering and it retains most of its interesting properties.

Keywords

Partial orderingsspreadmean residual life functiondispersive ordering

MSC classification

Primary: 62N05: Reliability and life testing
Secondary: 62E10: Characterization and structure theory
Type
Short Communications
Information
Journal of Applied Probability , Volume 35 , Issue 1 , March 1998 , pp. 221 - 228
Copyright
Copyright © Applied Probability Trust 1998 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Ahmed, A.N., Alzaid, A., Bartoszewicz, J., and Kochar, S.C. (1986). Dispersive and superadditive ordering. Adv. Appl. Prob. 18, 1019–1022.Google Scholar
Bagai, I., and Kochar, S.C. (1986). On tail ordering and comparison of failure rates. Commun. Statist. Theor. Meth. 15, 1377–1388.Google Scholar
Hollander, M., and Proschan, F. (1984). Nonparametric concepts and methods in reliability. In Handbook of Statistics, Nonparametric Methods 4. ed. Krishnaiah, P.R. and Sen, P.K. North Holland, Amsterdam. pp 613–655.Google Scholar
Joag-dev, K., Kochar, S., and Proschan, F. (1995). A general composition theorem and its applications to certain partial orderings of distributions. Statist. Prob. Lett. 22, 111–119.CrossRefGoogle Scholar
Kochar, S. (1989). On extensions of DMRL and related partial orderings of life distributions. Commun. Statist.-Stoch. Models 5, 235–245.Google Scholar
Kochar, S., and Wiens, D. (1987). Partial orderings of life distributions with respect to their aging properties. Naval Res. Logist. 34, 823–829.3.0.CO;2-R>CrossRefGoogle Scholar
Muñoz-Pérez, J. (1990). Dispersive ordering by the spread function. Statist. Prob. Lett. 10, 407–410.CrossRefGoogle Scholar
Pyke, R. (1965). Spacings. J. R. Statist. Soc. B 27, 395–436.Google Scholar
Shaked, M., and Shanthikumar, J.G. (1994). Stochastic Orders and their Applications. Academic Press, San Diego, CA.Google Scholar
van Zwet, W. (1964). Convex Transformation of Random Variables. Mathematisch Centrum, Amsterdam.Google Scholar