Duration Distribution and Up-crossings Rate of Generalized Hyperbolic Processes

Moh’d T. Alodat; Khalid M. Aludaat

doi:10.17713/ajs.v36i3.332

Authors

Moh’d T. Alodat Department of Statistics, Yarmouk University, Irbid, Jordan
Khalid M. Aludaat Department of Statistics, Yarmouk University, Irbid, Jordan

DOI:

https://doi.org/10.17713/ajs.v36i3.332

Abstract

A Gaussian process is usually used to model the sea surface elevation in the oceanography. As the depth of the water decreases or the sea severity increases, the sea surface elevation departs from symmetry and Gaussianity. In this paper, a stationary non-Gaussian random process called the generalized hyperbolic process is used as an alternative model. The process generates a family of processes. We derive the rate of up-crossings for this process and the distribution of the height of the process. We also derive the duration distribution of an excursion for the generalized hyperbolic process.

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