Role of concomitants of order statistics in determining parent bivariate distributions

ABSTRACT

In this paper, we establish the role of concomitants of order statistics in the unique identification of the parent bivariate distribution. From the results developed, we have illustrated by examples the process of determination of the parent bivariate distribution using a marginal pdf and the pdf of either of the concomitant of largest or smallest order statistic on the other variable. An application of the results derived in modeling of a bivariate distribution for data sets drawn from a population as well is discussed.

KEYWORDS:

• Bivariate distributions
• concomitants of order statistics
• generalized Morgenstern family of bivariate distributions
• Gumbel’s bivariate exponential distribution
• identification of bivariate distributions
• Morgenstern family of bivariate distributions

MATHEMATICS SUBJECT CLASSIFICATION:

• 60E15
• 62E15
• 62G30

Acknowledgments

The second author of the manuscript acknowledges the Kerala State Council for Science, Technology and Environment for providing financial assistance to this work in the form of Emeritus Scientist Fellowship. The authors express their gratefulness to the comments and constructive suggestions made on the earlier version of the paper by the learned reviewers. The authors express their thanks to some of the useful suggestions of the associate editor as well.