Extremal and additive processes generated by Pareto distributed random vectors. (15th October 2014)

• Record Type: Journal Article
• Authors: Mitov, Kosto V.; Nadarajah, Saralees
• Is Part Of: ESAIM. Volume 18(2014)
• Page Start: 667
• Page End: 685
• Publication Date: 2014-10-15
• Subjects: Additive process, -- extremal process, -- limit theorems, -- pareto distribution; Probabilities -- Periodicals; Mathematical statistics -- Periodicals; 519.2
• DOI: 10.1051/ps/2014001
• Languages: English
• ISSNs: 1292-8100

Abstract

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.