The Distribution of Argmaximum or a Winner Problem
| Autor: | Davydov, Youri, Rotar, Vladimir |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We consider a limit theorem for the distribution of a r.v. $Y_n:=argmax {\{X_i, i= 1,..., n\}},$ where $X_i'$s are independent continuous non-negative random variables. The r.v.'s $\{X_i, i=1,..., n\}$, may be interpreted as the gains of $n$ players in a game, and the r.v. $Y_n$ itself as the number of a ``winner". In the case of i.i.d.r.v.'s, the distribution of $Y_n$ is, clearly, uniform on $\{1,..., n\},$ while when the $X'$s are non-identically distributed, the problem requires some calculations. Comment: 11 pages |
| Databáze: | arXiv |
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