An order-statistics-based method for constructing multivariate distributions with fixed marginals

Baker, RD

Abstract

A new system of multivariate distributions with fixed marginal distributions is introduced via the consideration of random variates that are randomly chosen pairs of order statistics of the marginal distributions. The distributions allow arbitrary positive or negative Pearson correlations between pairs of random variates and generalise the Farlie–Gumbel–Morgenstern distribution. It is shown that the copulas of these distributions are special cases of the Bernstein copula. Generation of random numbers from the distributions is described, and formulas for the Kendall and grade (Spearman) correlations are given. Procedures for data fitting are described and illustrated with examples.

Citation

Baker, R. (2008). An order-statistics-based method for constructing multivariate distributions with fixed marginals. Journal of Multivariate Analysis, 99(10), 2312-2327. https://doi.org/10.1016/j.jmva.2008.02.019

• Journal Article Type: Article
• Publication Date: Jan 1, 2008
• Deposit Date: Nov 24, 2011
• Journal: Journal of Multivariate Analysis
• Print ISSN: 0047-259X
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 99
• Issue: 10
• Pages: 2312-2327
• DOI: https://doi.org/10.1016/j.jmva.2008.02.019
• Publisher URL: http://dx.doi.org/10.1016/j.jmva.2008.02.019