Geodesic
Reconstruction of the general distribution by the distribution of some
Teoriâ veroâtnostej i ee primeneniâ, Tome 49 (2004) no. 1, pp. 3-20

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We investigate the problem of characterizing the distribution of independent identically distributed random variables $X_1,\ldots,X_m$ (general distribution) by the distribution of linear statistics and statistics of maximum with positive coefficients. Necessary and sufficient conditions are found under which such a characterization takes place.
Keywords: characterization of distributions by the distributions of statistics, linear statistics, statistics of maximum. 
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     author = {D. V. Belomestny},
     title = {Reconstruction of the general distribution by the distribution of some},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {3--20},
     publisher = {mathdoc},
     volume = {49},
     number = {1},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2004_49_1_a0/}
}
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D. V. Belomestny. Reconstruction of the general distribution by the distribution of some. Teoriâ veroâtnostej i ee primeneniâ, Tome 49 (2004) no. 1, pp. 3-20. http://geodesic.mathdoc.fr/item/TVP_2004_49_1_a0/