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

01/30/2018

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by   Van Minh Nguyen, et al.

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For a sequence of random variables (X_1, X_2, ..., X_n), n ≥ 1, that are independent and identically distributed with a regularly varying tail with index -α, α≥ 0, we show that the contribution of the maximum term M_n (X_1,...,X_n) in the sum S_n X_1 + ... +X_n, as n →∞, decreases monotonically with α in stochastic ordering sense.