Characterizing the distributions of the random variables \(X_ 1,X_ 2,X_ 3\) by the distribution of \((X_ 1-X_ 3,X_ 2-X_ 3)\)
Let \(X_ 1,X_ 2,X_ 3\) be independent random variables. In this paper we investigate under which conditions the distribution of the random vector \((X_ 1-X_ 3,X_ 2-X_ 3)\) determines the distributions of \(X_ 1,X_ 2,X_ 3\) up to a change of the location. For a class of random variables a necessary and sufficient condition is given.
scientific article; zbMATH DE number 3930019
scientific article