An arrangement increasing property of the Marshall-Olkin bivariate exponential

A real-valued function g of two vector arguments u and v is said to be arrangement increasing if it increases in value as the components of u and v become more similarly arranged. Let X = (X1, X2) have the Marshall-Olkin bivariate exponential distribution with parameters [lambda]1, [lambda]2 and [lambda]12. If [theta]i = 1/[lambda]i for i = 1, 2, then it is shown that R = c1X1 + c2X2 is stochastically arrangement increasing in c = (c1, c2) and [theta] = ([theta]1, [theta]2).