Geodesic
On samples with identically distributed linear statistics
Teoriâ veroâtnostej i ee primeneniâ, Tome 20 (1975) no. 3, pp. 668-672

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Necessary and sufficient conditions are given for the characterization of the normal law by the property that the distributions of two linear statistics of type (0) with equal maximal moduli of coefficients (condition (4)) coincide. This result supplements wellknown Yu. V. Linnik's characterization theorem (see [1], Theorem 1) under conditions on the coefficients opposite to mentioned above. 
@article{TVP_1975_20_3_a20,
     author = {A. A. Zinger},
     title = {On samples with identically distributed linear statistics},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {668--672},
     publisher = {mathdoc},
     volume = {20},
     number = {3},
     year = {1975},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1975_20_3_a20/}
}
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A. A. Zinger. On samples with identically distributed linear statistics. Teoriâ veroâtnostej i ee primeneniâ, Tome 20 (1975) no. 3, pp. 668-672. http://geodesic.mathdoc.fr/item/TVP_1975_20_3_a20/