| Issue |
ESAIM: PS
Volume 18, 2014
|
|
|---|---|---|
| Page(s) | 667 - 685 | |
| DOI | https://doi.org/10.1051/ps/2014001 | |
| Published online | 15 October 2014 | |
Extremal and additive processes generated by Pareto distributed random vectors
1
Aviation Faculty, NMU, 5856 D. Mitropolia, Pleven, Bulgaria
kmitov@yahoo.com
2
School of Mathematics, University of Manchester,
Manchester, M13 9PL, UK
mbbsssn2@manchester.ac.uk
Received: 22 April 2013
Revised: 8 November 2013
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.
Mathematics Subject Classification: 62E20
Key words: Additive process / extremal process / limit theorems / pareto distribution
© EDP Sciences, SMAI, 2014
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