The main idea of conditional ordering is to sharpen the ordering results in such a way that even conditionally on some kind of additional information on the underlying “experiment” the ordering is valid. In this paper, some sufficient conditions for conditional variability and conditional dispersion orderings are established. The main idea is to find sufficient assumptions which are stable by conditioning.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
A.N. Ahmed, A. Alzaid, J. Bartoszewicz and S.C. Kochar, Dispersive and superadditive ordering, Adv. Appl. Prob. 18(1986)1019–1022.
E. Arjas, A stochastic process approach to multivariate reliability systems: Notions based on conditional stochastic order. Math. Oper. Res. 6(1981)263–276.
E. Arjas, The failure and hazard processes in multivariate reliability systems. Math. Oper. Res. 6(1981)551–562.
E. Arjas and I. Norros, Life lengths and association: A dynamic approach, Math. Oper. Res. 9(1984)151–158.
R.E. Barlow and F. Proschan,Statistical Theory of Reliability and Life Testing (Holt, Rinehart and Winston, 1978).
J. Bartoszewicz, Dispersive ordering and monotone failure rate distributions, Adv. Appl. Prob. 17(1985)472–474.
J. Bartoszewicz, A note on dispersive ordering defined by hazard functions, Statist. Prob. Lett. 6(1987)13–16.
A. Ibragimov, On the composition of unimodal distributions, Theory Prob. Appl. 1(1956)255–260.
S. Karlin,Total Positivity (Standford University Press, 1968).
J. Keilson,Markov Chain Models—Rarity and Exponentiality (Springer, 1979).
J. Keilson and U. Sumita, Uniform stochastic ordering and related inequalities, Can. J. Statist. 10(1982)181–198.
J. Lynch, G. Mimmack and F. Proschan, Dispersive ordering results, Adv. Appl. Prob. 15(1983) 889–891.
J. Lynch, G. Mimmack and F. Proschan Uniform stochastic ordering and total positivity, Can. J. Statist. 15(1987)63–69.
H. Oja, On location, scale, skewness and kurtosis of univariate distributions. Scand. J. Statist. 8(1981)154–168.
L. Rüschendorf, Conditional stochastic order and partial sufficiency, Adv. Appl. Prob. 23(1991) 46–63.
D.J. Saunders, Dispersive ordering of distributions, Adv. Appl. Prob. 16(1984)693–694.
M. Shaked, Dispersive ordering of distributions, J. Appl. Prob. 19(1982)310–320.
M. Shaked and J.G. Shanthikumar, Multivariate hazard rates and stochastic ordering, Adv. Appl. Prob. 19(1987)123–137.
D. Stoyan,Comparison Methods for Queues and other Stochastic Models (Wiley, 1983).
W. Whitt, Uniform conditional stochastic order, J. Appl. Prob. 17(1980)112–123.
W. Whitt, Multivariate monotone likelihood ratio and uniform conditional stochastic order, J. Appl. Prob. 19(1982)695–701.
W. Whitt, Uniform conditional variability ordering of probability distributions, J. Appl. Prob. 22(1985)619–633.
About this article
Cite this article
Metzger, C., Rüschendorf, L. Conditional variability ordering of distributions. Ann Oper Res 32, 127–140 (1991). https://doi.org/10.1007/BF02204831
- Main Idea
- Dispersion Ordering
- Sufficient Assumption
- Conditional Variability
- Conditional Dispersion