Geodesic
A~lemma on random determinants and its applications to characterizing multivariate distributions
Teoriâ veroâtnostej i ee primeneniâ, Tome 10 (1965) no. 4, pp. 755-758

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Sufficient conditions for the distribution of the random variables $v_j^{(i)}$ to be determined uniquely given the distribution of the determinant $$ \det\|v_j^{(i)}\| $$ are found. The result is applied to the testing of hypotheses about the type of the distribution on the basis of a sample from a multivariate distribution. 
@article{TVP_1965_10_4_a16,
     author = {Ts. G. Khakhubiya},
     title = {A~lemma on random determinants and its applications to characterizing multivariate distributions},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {755--758},
     publisher = {mathdoc},
     volume = {10},
     number = {4},
     year = {1965},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1965_10_4_a16/}
}
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Ts. G. Khakhubiya. A~lemma on random determinants and its applications to characterizing multivariate distributions. Teoriâ veroâtnostej i ee primeneniâ, Tome 10 (1965) no. 4, pp. 755-758. http://geodesic.mathdoc.fr/item/TVP_1965_10_4_a16/