Stochastic ordering of medians in exchangeable trivariate normal vectors

In this paper, we establish the stochastic ordering of median from an exchangeable trivariate normal vector based on the strength of the correlation coefficient. Specifically, by considering two exchangeable trivariate normal vectors with different correlation coefficients, 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.