Extremal and additive processes generated by Pareto distributed random vectors
ESAIM: Probability and Statistics, Tome 18 (2014) , pp. 667-685.

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.

DOI : https://doi.org/10.1051/ps/2014001
Classification : 62E20
Mots clés : additive process, extremal process, limit theorems, pareto distribution
@article{PS_2014__18__667_0,
author = {Mitov, Kosto V. and Nadarajah, Saralees},
title = {Extremal and additive processes generated by Pareto distributed random vectors},
journal = {ESAIM: Probability and Statistics},
pages = {667--685},
publisher = {EDP-Sciences},
volume = {18},
year = {2014},
doi = {10.1051/ps/2014001},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ps/2014001/}
}
Mitov, Kosto V.; Nadarajah, Saralees. Extremal and additive processes generated by Pareto distributed random vectors. ESAIM: Probability and Statistics, Tome 18 (2014) , pp. 667-685. doi : 10.1051/ps/2014001. http://www.numdam.org/articles/10.1051/ps/2014001/

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