Extremal and additive processes generated by Pareto distributed random vectors

Kosto V. Mitov; Saralees Nadarajah

ESAIM: Probability and Statistics (2014)

  • Volume: 18, page 667-685
  • ISSN: 1292-8100

Abstract

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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.

How to cite

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Mitov, Kosto V., and Nadarajah, Saralees. "Extremal and additive processes generated by Pareto distributed random vectors." ESAIM: Probability and Statistics 18 (2014): 667-685. <http://eudml.org/doc/274388>.

@article{Mitov2014,
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.},
author = {Mitov, Kosto V., Nadarajah, Saralees},
journal = {ESAIM: Probability and Statistics},
keywords = {additive process; extremal process; limit theorems; pareto distribution; Pareto distribution},
language = {eng},
pages = {667-685},
publisher = {EDP-Sciences},
title = {Extremal and additive processes generated by Pareto distributed random vectors},
url = {http://eudml.org/doc/274388},
volume = {18},
year = {2014},
}

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
PB - EDP-Sciences
VL - 18
SP - 667
EP - 685
AB - 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.
LA - eng
KW - additive process; extremal process; limit theorems; pareto distribution; Pareto distribution
UR - http://eudml.org/doc/274388
ER -

References

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