Hostname: page-component-84b7d79bbc-tsvsl Total loading time: 0 Render date: 2024-07-29T08:26:55.444Z Has data issue: false hasContentIssue false
  • English
  • Français

Uniform conditional stochastic order

Published online by Cambridge University Press:  14 July 2016

Ward Whitt
Ward Whitt*
Affiliation:
Bell Laboratories
*
∗Postal address: Bell Laboratories, Holmdel, NJ 07733, U.S.A.
Get access Rights & Permissions [Opens in a new window]

Abstract

One probability measure is less than or equal to another in the sense of UCSO (uniform conditional stochastic order) if a standard form of stochastic order holds for each pair of conditional probability measures obtained by conditioning on appropriate subsets. UCSO can be applied to the comparison of lifetime distributions or the comparison of decisions under uncertainty when there may be reductions in the set of possible outcomes. When densities or probability mass functions exist on the real line, then the main version of UCSO is shown to be equivalent to the MLR (monotone likelihood ratio) property. UCSO is shown to be preserved by some standard probability operations and not by others.

Keywords

STOCHASTIC ORDERCONDITIONAL PROBABILITYMONOTONE LIKELIHOOD RATIO
Type
Research Papers
Information
Journal of Applied Probability , Volume 17 , Issue 1 , March 1980 , pp. 112 - 123
Copyright
Copyright © Applied Probability Trust 1980 

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

Barlow, R. E. and Proschan, F. (1975) Statistical Theory of Reliability and Life Testing. Holt, Rinehart and Winston, New York.Google Scholar
Bawa, V. S. (1975) Optimal rules for ordering uncertain prospects. J. Financial Economics 2, 95–121.CrossRefGoogle Scholar
Billingsley, P. (1968) Convergence of Probability Measures. Wiley, New York.Google Scholar
Brumelle, S. L. and Vickson, R. G. (1975) A unified approach to stochastic dominance. Stochastic Optimization Models in Finance, ed. Ziemba, W. T. and Vickson, R. G., Academic Press, New York, 101–113.CrossRefGoogle Scholar
Ferguson, T. S. (1967) Mathematical Statistics, A Decision Theoretic Approach. Academic Press, New York.Google Scholar
Goroff, D. and Whitt, W. (1978) Continuity of the admissible set in stochastic dominance. Economics Discussion Paper, Bell Laboratories, Holmdel, New Jersey 07733.Google Scholar
Halmos, P. R. (1950) Measure Theory. Van Nostrand, Princeton, NJ.CrossRefGoogle Scholar
Kamae, T., Krengel, U. and O'brien, G. L. (1977) Stochastic inequalities on partially ordered spaces. Ann. Prob. 5, 899–912.CrossRefGoogle Scholar
Karlin, S. (1968) Total Positivity, Vol. I. Stanford University Press, Stanford, CA.Google Scholar
Lehmann, E. L. (1955) Ordered families of distributions. Ann. Math. Statist. 26, 399–419.CrossRefGoogle Scholar
Meyer, J. (1977) Choice among distributions. J. Economic Theory 14, 326–336.CrossRefGoogle Scholar
Meyer, P. A. (1966) Probability and Potentials. Blaisdell, Boston, MA.Google Scholar
Nachbin, L. (1965) Topology and Order. Van Nostrand, Princeton, NJ.Google Scholar
Strassen, V. (1965) The existence of probability measures with given marginals. Ann. Math. Statist. 36, 423–439.CrossRefGoogle Scholar