Journal article, 2009

Corresponding to n independent non-negative random variables X_1,...,X_n , are values M_1,...,M_n , where each M_i is the expected value of the maximum of n independent copies of X_i. We obtain an upper bound for the expected value of the maximum of X_1,...,X_n in terms of M_1,...,M_n . This inequality is sharp in the sense that the random variables can be chosen so that the bound is approached arbitrarily closely. We also present related comparison results.

Mixing - Stochastic ordering - Distribution of the maximum

Chalmers, Mathematical Sciences, Mathematical Statistics

University of Gothenburg

Chalmers

Monash University

Monash University

1386-1999 (ISSN)

Vol. 12 1 19-31Computational Mathematics

Probability Theory and Statistics

10.1007/s10687-008-0066-2