Some properties and characterizations for generalized multivariate Pareto distributions

Hsiaw-Chan Yeh

Journal of Multivariate Analysis, 2004, vol. 88, issue 1, 47-60

Abstract: In this paper, several distributional properties and characterization theorems of the generalized multivariate Pareto distributions are studied. It is found that the multivariate Pareto distributions have many mixture properties. They are mixed either by geometric, Weibull, or exponential variables. The multivariate Pareto, MP(k)(I), MP(k)(II), and MP(k)(IV) families have closure property under finite sample minima. The MP(k)(III) family is closed under both geometric minima and geometric maxima. Through the geometric minima procedure, one characterization theorem for MP(k)(III) distribution is developed. Moreover, the MP(k)(III) distribution is proved as the limit multivariate distribution under repeated geometric minimization. Also, a characterization theorem for the homogeneous MP(k)(IV) distribution via the weighted minima among the ordered coordinates is developed. Finally, the MP(k)(II) family is shown to have the truncation invariant property.

Keywords: Multivariate Pareto distributions MP(k)(I); MP(k)(II); MP(k)(III); MP(k)(IV) families Coordinatewise geometric minima Geometric maxima Characterizations Homogeneous MP(k)(IV) distribution Truncation Residual life (search for similar items in EconPapers)
Date: 2004
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (7)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0047-259X(03)00061-7
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:88:y:2004:i:1:p:47-60

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Journal of Multivariate Analysis is currently edited by de Leeuw, J.

More articles in Journal of Multivariate Analysis from Elsevier
Bibliographic data for series maintained by Catherine Liu ().