Contribution of the Extreme Term in the Sum of Samples with Regularly Varying Tail
Abstract
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 tail with index $\alpha$, $\alpha \geq 0$, we show that the contribution of the maximum term $M_n \triangleq \max(X_1,\ldots,X_n)$ in the sum $S_n \triangleq X_1 + \cdots +X_n$, as $n \to \infty$, decreases monotonically with $\alpha$ in stochastic ordering sense.
 Publication:

arXiv eprints
 Pub Date:
 January 2018
 arXiv:
 arXiv:1801.09887
 Bibcode:
 2018arXiv180109887N
 Keywords:

 Mathematics  Probability;
 Computer Science  Information Theory;
 60G70;
 60G50;
 60E15;
 90B15
 EPrint:
 9 pages, submitted for possible publication