Abstract
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 \({\frac{(Z - W)}{(Z + W)}}\) and (Z + W) are independent if and only if X and Y have gamma distribution.
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The research was conducted by the research fund of Dankook University in 2011.
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Lee, MY., Galambos, J. A Kotz and Steutel type of characterization of the gamma family. Aequat. Math. 84, 121–124 (2012). https://doi.org/10.1007/s00010-012-0147-9
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DOI: https://doi.org/10.1007/s00010-012-0147-9