Abstract
Let X, Y = ( Y 1 , . . . , Ym), Z = ( Z 1 . . . . . Z , ) be three independent random vectors of total dimension 1 + m + n with nonvanishing characteristic functions. Denote T I = X + Y j , j = l , . . . , m ; U k = X Z k , k = l . . . . ,n . Then ( T , U ) = (7"1 . . . . . T~, U1 . . . . . U,) is an (m + n)-dimensional random vector. It is known that the distribution of (T, U) determines the distributions of X, Y, Z up to shifts (see [1], Corollary 1). In this paper two theorems on similar characterizations are given, the sums and differences are replaced by maxima and minima of the corresponding pairs of random variables. Throughout this paper we shall denote for q , c2 real
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