Best-Possible Bounds on Sets of Multivariate Distribution Functions

If H denotes the joint distribution function of n random variables X 1 , X 2 ,..., X n whose margins are F 1 , F 2 ,..., F n , respectively, then the fundamental best-possible bounds inequality for H is F 2 (x 2 ),..., F n (x n )) for all x 1 , x 2 ,..., x n in [−∞, ∞]. In this paper we employ n-cop...

Full description

Saved in:
Bibliographic Details
Published in:Communications in statistics. Theory and methods 2005-01, Vol.33 (4), p.805-820
Main Authors: Rodríguez-Lallena, José Antonio, Úbeda-Flores, Manuel
Format: Article
Language:English
Subjects:
Bounds
Copulas
Distribution functions
Quasi-copulas
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:If H denotes the joint distribution function of n random variables X 1 , X 2 ,..., X n whose margins are F 1 , F 2 ,..., F n , respectively, then the fundamental best-possible bounds inequality for H is F 2 (x 2 ),..., F n (x n )) for all x 1 , x 2 ,..., x n in [−∞, ∞]. In this paper we employ n-copulas and n-quasi-copulas to find similar bounds on arbitrary sets of multivariate distribution functions with given margins. We discuss bounds for an n-quasi-copula Q when a value of Q at a single point is known. As an application, we investigate about bounds for a multivariate distribution function H with given univariate margins when the value of H is known at a single point whose coordinates are percentiles of the variables X 1 , X 2 ,..., X n , respectively.
ISSN:0361-0926
1532-415X
DOI:10.1081/STA-120028727