Teoriâ veroâtnostej i ee primeneniâ, Tome 10 (1965) no. 3, pp. 479-487
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Yu. V. Prokhorov. On a characterisation of a class of probability distributions by those of some statistics. Teoriâ veroâtnostej i ee primeneniâ, Tome 10 (1965) no. 3, pp. 479-487. http://geodesic.mathdoc.fr/item/TVP_1965_10_3_a5/
@article{TVP_1965_10_3_a5,
author = {Yu. V. Prokhorov},
title = {On a~characterisation of a~class of probability distributions by those of some statistics},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {479--487},
year = {1965},
volume = {10},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1965_10_3_a5/}
}
TY - JOUR
AU - Yu. V. Prokhorov
TI - On a characterisation of a class of probability distributions by those of some statistics
JO - Teoriâ veroâtnostej i ee primeneniâ
PY - 1965
SP - 479
EP - 487
VL - 10
IS - 3
UR - http://geodesic.mathdoc.fr/item/TVP_1965_10_3_a5/
LA - ru
ID - TVP_1965_10_3_a5
ER -
%0 Journal Article
%A Yu. V. Prokhorov
%T On a characterisation of a class of probability distributions by those of some statistics
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1965
%P 479-487
%V 10
%N 3
%U http://geodesic.mathdoc.fr/item/TVP_1965_10_3_a5/
%G ru
%F TVP_1965_10_3_a5
Let $\mathscr P$ be a class of probability distributions of random element $X$. The question is whether there exist a statistic $Y=f(X)$ possesing two following properties: 1$^\circ$. Its distribution $Q_P^Y$ under $P\in\mathscr P$ does not depend on $P$, $Q_P^Y=Q_\mathscr P^Y$. 2$^\circ$. If for some $P'$$Q_{P'}^Y=Q_\mathscr P^Y$ then $P'\in\mathscr P$. The question is solved positively for some special families $\mathscr P$.
