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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

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