The mixing advantage is less than 2 |
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| Authors: | Kais Hamza Peter Jagers Aidan Sudbury Daniel Tokarev |
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| Institution: | (1) School of Mathematical Sciences, Monash University, Clayton, Australia;(2) Mathematical Statistics, Chalmers University of Technology, Gothenburg, Sweden |
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| Abstract: | 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.
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| Keywords: | Mixing Stochastic ordering Distribution of the maximum |
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