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.
|Pages (from-to)||19 - 31|
|Number of pages||13|
|Publication status||Published - 2009|