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

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.