Geodesic
Reconstituting the distribution of the components of a~random Vector from distributions of certain statistics
Matematičeskie zametki, Tome 13 (1973) no. 6, pp. 889-892.

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Let $(X_1,\dots,X_n)$ be a random vector with independent components. It is proven in this paper that, under certain restrictions, the distributions of the pair $S_1=\sup(a_1X_1,\dots,a_nX_n)$ and $S_2=\sup(b_1X_1,\dots,b_nX_n)$ univocally define the distribution function of the components $X_j$. 
@article{MZM_1973_13_6_a10,
     author = {L. B. Klebanov},
     title = {Reconstituting the distribution of the components of a~random {Vector} from distributions of certain statistics},
     journal = {Matemati\v{c}eskie zametki},
     pages = {889--892},
     publisher = {mathdoc},
     volume = {13},
     number = {6},
     year = {1973},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1973_13_6_a10/}
}
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L. B. Klebanov. Reconstituting the distribution of the components of a~random Vector from distributions of certain statistics. Matematičeskie zametki, Tome 13 (1973) no. 6, pp. 889-892. http://geodesic.mathdoc.fr/item/MZM_1973_13_6_a10/