The mixing advantage is less than 2

Kais Hamza; Peter Jagers; Aidan Sudbury; Daniel Tokarev

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arXiv · 0805.0447

The mixing advantage is less than 2

Kais Hamza·Peter Jagers·Aidan Sudbury·Daniel Tokarev

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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 to 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 quantity and its bound can be made as close to each other as we want. We also present related comparison results.

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Kais Hamza, Peter Jagers, Aidan Sudbury, Daniel Tokarev. 2008-05-04. The mixing advantage is less than 2. https://arxiv.org/abs/0805.0447

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