Stochastic Ordering of Medians in Equi-Correlated Trivariate Normal Vectors Based on the Correlation Coefficient

In this paper, we establish the stochastic ordering of median from an equi-correlated trivariate normal vector based on the strength of the correlation coefficient. Specifically, by considering two equi- correlated trivariate normal vectors with different correlation coefficient, we show that the absolute value of the median in the vector with smaller correlation coefficient is stochastically smaller than the absolute value of the median in the vector with larger correlation coefficient . We prove this result by utilizing skew-normal distributions.