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.
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/}
}
TY - JOUR AU - Mitov, Kosto V. AU - Nadarajah, Saralees TI - Extremal and additive processes generated by Pareto distributed random vectors JO - ESAIM: Probability and Statistics PY - 2014 SP - 667 EP - 685 VL - 18 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ps/2014001/ DO - 10.1051/ps/2014001 LA - en ID - PS_2014__18__667_0 ER -
%0 Journal Article %A Mitov, Kosto V. %A Nadarajah, Saralees %T Extremal and additive processes generated by Pareto distributed random vectors %J ESAIM: Probability and Statistics %D 2014 %P 667-685 %V 18 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ps/2014001/ %R 10.1051/ps/2014001 %G en %F PS_2014__18__667_0
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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