Comparisons of Parallel Systems According to the Convex Transform Order

A parallel system with heterogeneous exponential component lifetimes is shown to be more skewed (according to the convex transform order) than the systemwith independent and identically distributed exponential components. As a consequence, equivalent conditions for comparing the variabilities of the largest order statistics fromheterogeneous and homogeneous exponential samples in the sense of the dispersive order and the rightspread order are established. A sufficient condition is also given for the proportional hazard rate model.