Convergence of exceedance point processes of normal sequences with a seasonal component and its applications

In this paper, we prove that, under some mild conditions, a time-normalized point process of exceedances by a nonstationary and strongly dependent normal sequence with a seasonal component converges in distribution to the in plane Cox process. As an application of the convergence result, we deduce t...

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Bibliographic Details
Published in:Journal of inequalities and applications 2016-05, Vol.2016 (1), p.1-10, Article 141
Main Authors: Jiang, Yingying, Li, Baokun, Lin, Fuming
Format: Article
Language:English
Subjects:
Analysis
Applications of Mathematics
Convergence
exceedance point process
in plane Cox process
Inequalities
kth maxima
Mathematics
Mathematics and Statistics
nonstationary sequences with a seasonal component
Planes
Statistics
strongly dependent normal sequences
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Summary:In this paper, we prove that, under some mild conditions, a time-normalized point process of exceedances by a nonstationary and strongly dependent normal sequence with a seasonal component converges in distribution to the in plane Cox process. As an application of the convergence result, we deduce two important joint limit distributions for the order statistics.
ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-016-1082-4