RESEARCH ARTICLE


Statistical Properties of the Periodogram for Stable Random Field



M.A. Ghazal*
Department of Mathematics, Faculty of Science, Mansoura University, New Damietta, Egypt.


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© 2009 Ghazal et al.;

open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: https://creativecommons.org/licenses/by/4.0/legalcode. This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

* Address correspondence to this author at the Department of Mathematics, Faculty of Science, Mansoura University, New Damietta, Egypt. E-mail: maghazal@yahoo.com


Abstract

Let X(t) (t ∈ Z) be a discrete stable random field. The problem of estimating the spectral density field based on X(t) is considered. Moments and the asymptotic moments of the spectral sample, the periodogram, based on X(t) are calculated.

Keywords: Stable distributions, stationary stable processes, spectral representation, symmetric stable distribution, stable random field, periodogram..