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On uniform conditional stochastic order conditioned on planar regions

Published online by Cambridge University Press:  14 July 2016

J. George Shanthikumar  and
Hui-Wen Koo
J. George Shanthikumar*
Affiliation:
University of California, Berkeley
Hui-Wen Koo*
Affiliation:
Bellcore
*
∗Postal address: School of Business Administration, University of California, Berkeley CA 94720, USA.
∗∗Postal address: Bellcore, Bell Communications Research 290 West Mt. Pleasant Avenue Livingston, NJ 07039, USA.
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Abstract

Sufficient conditions under which two random vectors are ordered in the sense of uniform conditional stochastic order (Whitt (1980), (1982)) with respect to planar regions are given. A natural classification of distributions based on this notion of stochastic order is defined and studied. A negative dependence property of Block et al. (1985) is shown to hold for this class of distributions. An application of these results in statistics is also presented.

Keywords

MTP2NEGATIVE DEPENDENCEAUCTION THEORY
Type
Research Papers
Information
Journal of Applied Probability , Volume 27 , Issue 1 , March 1990 , pp. 115 - 123
Copyright
Copyright © Applied Probability Trust 1990 

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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 by 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
Barlow, R. E. and Proschan, F. (1981) Statistical Theory of Reliability and Life Testing. To begin with, Silver Spring, MD.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
Holley, R. (1974) Remarks on the FKG inequalities. Comm. Math. Phys. 36, 227–231.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. and Rinott, Y. (1980) Classes of orderings of measures and related correlation inequalities: I. Multivariate totally positive distributions. J. Multivariate Anal. 10, 467–498.Google Scholar
Kemperman, J. H. B. (1973) On the FKG inequality for measures on a partially ordered space. Indag. Math. 39, 313–331.Google Scholar
Koo, Hui-Wen (1988) An Analysis of Information Pooling when Joint Bidding or Collusion Occurs in the First-price Sealed Bidding. Ph.D. dissertation, School of Business Administration, University of California, Berkeley, CA 94720.Google Scholar
Norros, I. (1986) A compensator representation of multivariate life length distributions with applications. Scand. J. Statist. 13, 99–112.Google Scholar
Preston, C. J. (1974) A generalization of the FKG inequalities. Comm. Math. Phys. 36, 223–241.Google Scholar
Ross, S. M. (1983) Stochastic processes. Wiley, New York, NY.Google Scholar
Shaked, M. and Shanthikumar, J. G. (1987a) Multivariate hazard rates and stochastic ordering. Adv. Appl. Prob. 19, 123–137.Google Scholar
Shaked, M. and Shanthikumar, J. G. (1987b) The multivariate hazard construction. Stoch. Proc. Appl. 24, 241–258.Google Scholar
Shanthikumar, J. G. (1987) On stochastic comparison of random vectors. J. Appl. Prob. 24, 123–136.Google Scholar
Shanthikumar, J. G. and Yao, D. D. (1986a) The preservation of likelihood ratio ordering under convolution. Stoch. Proc. Appl. 23, 259–267.Google Scholar
Shanthikumar, J. G. and Yao, D. D. (1986b) The effect of increasing service rates in a closed queueing network. J. Appl. Prob. 23, 474–483.Google Scholar
Shanthikumar, J. G. and Yao, D. D. (1988) Second-order properties of the throughput of a closed queueing network. Math. Operat. Res. 13, 524–534.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
Whitt, W. (1980) Uniform conditional stochastic order. J. Appl. Prob. 17, 112–123.Google Scholar
Whitt, W. (1982) Multivariate monotone likelihood ratio and uniform conditional stochastic order. J. Appl. Prob. 19, 695–701.Google Scholar