A Kotz and Steutel type of characterization of the gamma family

作者：Lee Min Young^*; Galambos Janos

来源：Aequationes Mathematicae, 2012, 84(1-2): 121-124.

DOI：10.1007/s00010-012-0147-9

• Independent identically distributed
• scale-invariant statistics
• gamma distribution
• the characteristic function

Let X and Y be independent identically distributed (i.i.d.) nondegenerate and positive random variables with a common absolutely continuous distribution function F(x). We use the notation Z = max(X, Y) and W = min(X, Y). In the present paper, we prove that and (Z + W) are independent if and only if X and Y have gamma distribution.

• 出版日期2012-9