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Bivariate processes with positive or negative dependent structures

Published online by Cambridge University Press:  14 July 2016

Nader Ebrahimi
Nader Ebrahimi*
Affiliation:
Northern Illinois University
*
∗Postal address: Department of Mathematical Sciences, Northern Illinois University, DeKalb, IL 60115–2888, USA.
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Abstract

In this paper various notions of positive and negative dependence for bivariate stochastic processes are introduced and their interrelationship is studied. Examples are given to illustrate these concepts.

Keywords

PQDNQDRTIRTDPRDNRDASSOCIATED RANDOM VARIABLESBROWNIAN MOTION PROCESSPOISSON PROCESSRECORD VALUEHITTING TIME
Type
Research Papers
Information
Journal of Applied Probability , Volume 24 , Issue 1 , March 1987 , pp. 115 - 122
Copyright
Copyright © Applied Probability Trust 1987 

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References

Ahmed, A. N., Langberg, N. A., Leon, R. and Proschan, F. (1978) Two concepts of positive dependence, with applications in multivariate analysis. Tech. Report 78–6, Department of Statistics, Florida State University.10.21236/ADA067545Google Scholar
Barlow, R. D. and Proschan, R. (1975) Statistical Theory of Reliability and Life Testing: Probability Models. Holt, Rinehart and Winston, New York.Google Scholar
Berman, M. (1977) Some multivariate generalizations of results in univariate stationary processes. J. Appl. Prob. 14, 748–757.10.2307/3213348Google Scholar
Berman, M. (1978) Regenerative multivariate point processes. Adv. Appl. Prob. 10, 411–430.10.2307/1426943Google Scholar
Block, H. W., Savits, R. H. and Shaked, M. (1983) A concept of negative dependence using stochastic ordering. Technical Report, University of Pittsburgh, Pittsburgh, Pennsylvania.Google Scholar
Cox, D. R. and Isham, V. (1980) Point Processes. Chapman and Hall, London.Google Scholar
Ebrahimi, N. and Ghosh, M. (1981) Multivariate negative dependence. Commun. Statist. A10, 307–337.Google Scholar
Esary, J. D. and Proschan, R. (1972) Relationship among some concepts of bivariate dependence. Ann. Math. Statist. 43, 651–655.10.1214/aoms/1177692646Google Scholar
Esary, J. D., Proschan, F. and Walkup, D. W. (1967) Association of random variables, with applications. Ann. Math. Statist. 38, 1466–1474.10.1214/aoms/1177698701Google Scholar
Friday, D. S. (1981) Dependence concepts for stochastic processes. Proc. NATO Adv. Study Inst. Series 5, 349–361.Google Scholar
Glaz, J. and Johnson, B. M. (1982) Probability inequalities for multivariate distributions with dependence structures. Technical Report, University of Connecticut.Google Scholar
Lehmann, E. L. (1966) Some concepts of dependence. Ann. Math. Statist. 37, 1137–1153.10.1214/aoms/1177699260Google Scholar
Pitt, L. D. (1982) Positively correlated normal variables are associated. Ann. Prob. 10, 496–500.10.1214/aop/1176993872Google Scholar
Ross, S. M. (1983) Stochastic Processes. Wiley, New York.Google Scholar