The Distribution of Argmaximum or a Winner Problem
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866909094649004032 |
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| author | Davydov, Youri Rotar, Vladimir |
| author_facet | Davydov, Youri Rotar, Vladimir |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_05967 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The Distribution of Argmaximum or a Winner Problem Davydov, Youri Rotar, Vladimir Probability Primary 60F17, Secondary 60G15 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. |
| title | The Distribution of Argmaximum or a Winner Problem |
| topic | Probability Primary 60F17, Secondary 60G15 |
| url | https://arxiv.org/abs/2305.05967 |