Hostname: page-component-7b7567c8c-kwt9d Total loading time: 0 Render date: 2026-11-13T22:32:51.733Z Has data issue: false hasContentIssue false
  • English
  • Français

On stochastic comparison of random vectors

Published online by Cambridge University Press:  14 July 2016

J. George Shanthikumar
J. George Shanthikumar*
Affiliation:
University of California, Berkeley
*
∗Postal address: School of Business Administration, University of California, Berkeley, CA 94720, USA.
Get accessRights & Permissions [Opens in a new window]

Abstract

We provide sufficient conditions under which two random vectors could be stochastically compared using the standard construction. These conditions are weaker than those discussed by Arjas and Lehtonen (1978) and Veinott (1965). Using these conditions we present extensions of (i) a result of Block et al. (1984) concerning the stochastic monotonicity of independent and identically distributed random variables conditioned on their partial order statistics, and (ii) a theorem of Efron (1965) regarding an increasing property of Pólya frequency functions. Applications of these extensions are also pointed out.

Keywords

STOCHASTIC ORDERINGNEGATIVE DEPENDENCEPÓLYA FREQUENCY FUNCTIONCOMPONENT CANNIBALIZATION

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 24 , Issue 1 , March 1987, pp. 123 - 136
Copyright
Copyright © Applied Probability Trust 1987 

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.)

Article purchase

Temporarily unavailable

Footnotes

Supported by the Air Force Office of Scientific Research, U.S.A.F., under Grant AFOSR-84-0205. Reproduction in whole or in part is permitted for any purpose of the United States Government.

References

Arjas, E. and Lehtonen, T. (1978) Approximating many server queues by means of single server queues. Math. Operat. Res. 3, 205–223.Google Scholar
Block, H. W., Savits, T. H. and Shaked, M. (1985) A concept of negative dependence using stochastic ordering. Statist. Prob. Letters 3, 81–86.Google Scholar
Block, H. W., Bueno, V., Savits, T. H. and Shaked, M. (1984) Probability Inequalities via Negative Dependence for Random Variables Conditioned on Order Statistics. Technical Report, University of Pittsburgh.Google Scholar
Efron, B. (1965) Increasing properties of Pólya frequency functions. Ann. Math. Statist. 36, 272–279.Google Scholar
Kamae, T., Krengel, U. and O'Brien, G. L. (1977) Stochastic inequalities on partially ordered spaces. Ann. Prob. 5, 899–912.Google Scholar
Karlin, S. (1965) Total Positivity. Stanford University Press, Stanford.Google Scholar
Norros, I. (1984) A compensator representation of multivariate life length distributions, with applications.Google Scholar
Shaked, M. and Shanthikumar, J. G. (1985) Multivariate hazard construction. Technical Report, Dept. of Math., University of Arizona.Google Scholar
Shaked, M. and Shanthikumar, J. G. (1987) Multivariate hazard rates and stochastic ordering. Adv. Appl. Prob. 19, 123–137.Google Scholar
Shanthikumar, J. G. and Yao, D. D. W. (1985) Stochastic monotonicity of queue lengths in closed queueing networks. Operat. Res. To appear.Google Scholar
Shanthikumar, J. G. and Yao, D. D. W. (1986) The effect of increasing service rates in closed queueing networks. J. Appl. Prob. 23, 474–483.Google Scholar
Veinott, A. F. (1965) Optimal policy in a dynamic, single product, nonstationary inventory model with several demand classes. Operat. Res. 13, 761–778.Google Scholar