Identification of power distribution mixtures through regression of exponentials

Wen-Jang Huang () and Nan-Cheng Su ()

Statistical Papers, 2013, vol. 54, issue 1, 227-241

Abstract: Given two independent non-degenerate positive random variables X and Y, Lukacs (Ann Math Stat 26:319–324, 1955 ) proved that X/(X + Y) and X + Y are independent if and only if X and Y are gamma distributed with the same scale parameter. In this work, under the assumption X/U and U are independent, and X/U has a $${{\mathcal Be}(p,\,q)}$$ distribution, we characterize the distribution of (U, X) by the condition E(h(U − X)|X) = b, where h is allowed to be a linear combination of exponential functions. Since the assumption for X and U above is equivalent to X|U being $${\mathcal{B}e(p,\,1)}$$ scaled by U, hence our results can be viewed as identification of a power distribution mixture. Copyright Springer-Verlag 2013

Keywords: Beta distribution; Characterization; Constant regression; Conditional expectation; Gamma distribution; Mixture distributions; Primary 60E05; Secondary 62E10 (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s00362-011-0421-2

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