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For a sequence of random variables $(X_1, X_2, \ldots, X_n)$, $n \geq 1$,that are independent and identically distributed with a regularly varying tailwith index $-\alpha$, $\alpha \geq 0$, we show that the contribution of themaximum term $M_n \triangleq \max(X_1,\ldots,X_n)$ in the sum $S_n \triangleqX_1 + \cdots +X_n$, as $n \to \infty$, decreases monotonically with $\alpha$ instochastic ordering sense.

Contribution of the Extreme Term in the Sum of Samples with Regularly Varying Tail