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Extremal and additive processes generated by Pareto distributed random vectors

Published online by Cambridge University Press:  15 October 2014

Kosto V. Mitov  and
Saralees Nadarajah
Kosto V. Mitov
Affiliation:
Aviation Faculty, NMU, 5856 D. Mitropolia, Pleven, Bulgaria. [email protected]
Saralees Nadarajah
Affiliation:
School of Mathematics, University of Manchester, Manchester, M13 9PL, UK; [email protected]
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Abstract

Pareto distributions are most popular for modeling heavy tailed data. Here, we obtain weak limits of a sequence of extremal and a sequence of additive processes constructed by a series of Bernoulli point processes with bivariate Pareto space components. For the limiting processes we derive the one dimensional distributions in explicit forms. Some of the main properties of these distributions are also proved.

Keywords

Additive processextremal processlimit theoremspareto distribution
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 18 , 2014 , pp. 667 - 685
Copyright
© EDP Sciences, SMAI, 2014

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