Order statistics and their concomitants from multivariate normal mean–variance mixture distributions with application to Swiss Markets Data

ABSTRACT

In this article, by considering a multivariate normal mean–variance mixture distribution, we derive the exact joint distribution of linear combinations of order statistics and their concomitants. From this general result, we then deduce the exact marginal and conditional distributions of order statistics and their concomitants arising from this distribution. We finally illustrate the usefulness of these results by using a Swiss markets dataset.

KEYWORDS:

• Concomitants
• Multivariate generalized hyperbolic distribution
• Multivariate normal mean–variance mixture distribution
• Multivariate selection distribution
• Order statistics

MATHEMATICS SUBJECT CLASSIFICATION:

• 62H05
• 62H10
• 62E15

Acknowledgments

The authors express their sincere thanks to the anonymous referees for their suggestions and constructive comments which led to improvement in the content as well as presentation of this manuscript.