The distribution of argmaximum or a winner problem (Q6580278)

The authors consider a limit theorem for the distribution of a random variable \(A_n=\arg \max_{i=1,\dots,n} X_i\), where \(X_i\) are independent continuous non-negative random variables. The variables \(X_i, \; i=1,\dots,n,\) may be interpreted as the gains of \(n\) players in a game, and the random variable \(A_n\) itself as the number of a winner. The paper contains some limit theorems for the distribution of \(A_n\) as \(n \rightarrow \infty.\)