The distribution of argmaximum or a winner problem

Youri Davydov and Vladimir Rotar

Statistics & Probability Letters, 2024, vol. 211, issue C

Abstract: We consider a limit theorem for the distribution of a random variable (r.v.) An=argmaxi:1…n{Xi}, where Xi’s are independent continuous non-negative random r.v.’s. The Xi,i=1.…,n, may be interpreted as the gains of n players in a game, and the r.v. An itself as the number of a “winner”. The paper contains some limit theorems for the distribution of An as n→∞.

Keywords: Limit theorem; Maximum of random variables; Argmaximum (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1016/j.spl.2024.110152

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