A count-based nonparametric test on strict bivariate Stochastic arrangement increasing property

Abstract

As the extension of classical stochastic orders on univariate distributions, stochastic arrangement increasing (SAI) distributions of random vectors are found to be of important interest in actuarial risk, reliability theory and other related areas; However, the lack of a statistical method to detect such distributions blocks their application in real practice. In this paper, we propose a simple nonparametric test on the bivariate symmetry against the potential alternative of a strict bivariate SAI distribution. The null distribution and asymptotic behaviour of the testing statistic are studied, and the method is also utilized to detecting the potential pattern of multivariate SAI. The performance of the method is illustrated by using Monte Carlo simulation, and the method is also applied to two real data sets as applications as well.

Keywords:

• Binomial distribution
• Copula
• exchangeability
• Marshall-Okin distribution
• stochastic orders
• symmetry

Acknowledgments

The authors would like to thank the two anonymous reviewers for not only providing insightful comments, inspired by which we come up with the current more comprehensive version, but also directing us to the recent research on testing circular and axis symmetry due to Rattihalli et al. [45] and Riahi and Patil [44], which aroused our interest to go further in this line.

Disclosure statement

No potential conflict of interest was reported by the author(s).