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Duration Distribution of the Conjunction of Two Independent F Processes

Part of: Stochastic processes

Published online by Cambridge University Press:  14 July 2016

M. T. Alodat ,
M. Al-Rawwash  and
M. A. Jebrini
M. T. Alodat*
Affiliation:
Yarmouk University
M. Al-Rawwash*
Affiliation:
Yarmouk University
M. A. Jebrini*
Affiliation:
Yarmouk University
*
∗Postal address: Department of Statistics, Yarmouk University, Irbid, Jordan.
∗Postal address: Department of Statistics, Yarmouk University, Irbid, Jordan.
∗Postal address: Department of Statistics, Yarmouk University, Irbid, Jordan.
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Abstract

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In this paper we obtain an approximation for the duration distribution of the excursion set generated by the minimum of two independent F random processes above a high threshold u. Moreover, we obtain a closed-form approximation for the mean duration of the conjunction of these two F processes. As an illustration, we conduct a simulation study to compare the performances of the approximated distribution and the exact distribution.

Keywords

Conjunctiondowncrossingduration distributionexcursion setF processGaussian processupcrossing

MSC classification

Secondary: 60G10: Stationary processes 60G15: Gaussian processes
Type
Research Article
Information
Journal of Applied Probability , Volume 47 , Issue 1 , March 2010 , pp. 179 - 190
Copyright
Copyright © Applied Probability Trust 2010 

References

Aldous, D. (1989). Probability Approximations via the Poisson Clumping Heuristic. Springer, New York.Google Scholar
Alodat, M. T. (2004). Detecting conjunctions using cluster volumes. , McGill University.Google Scholar
Cao, J. (1999). The size of the connected components of excursion sets of χ2, t and f fields. Adv. Appl. Prob. 31, 579–595.Google Scholar
Leadbetter, M. R., Lindgren, G. and Rootzén, H. (1983). Extremes and Related Properties of Random Sequences and Processes. Springer, New York.CrossRefGoogle Scholar
Robert, C. P. and Casella, G. (1999). Monte Carlo Statistical Methods. Springer, New York.Google Scholar
Worsley, K. J. (1994). Local maxima and the expected Euler characteristic of excursion sets of χ2, t and f fields. Adv. Appl. Prob. 26, 13–42.Google Scholar
Worsley, K. J. and Friston, K. J. (2000). A test for a conjunction. Statist. Prob. Lett. 47, 135–140.Google Scholar