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Identification of power distribution mixtures through regression of exponentials

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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.

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Authors and Affiliations

  1. Department of Applied Mathematics, National University of Kaohsiung, Kaohsiung, 81148, Taiwan

    Wen-Jang Huang

  2. Department of Statistics, National Cheng-Kung University, Tainan, 70101, Taiwan

    Nan-Cheng Su

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  1. Wen-Jang Huang
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  2. Nan-Cheng Su
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Correspondence to Wen-Jang Huang.

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Huang, WJ., Su, NC. Identification of power distribution mixtures through regression of exponentials. Stat Papers 54, 227–241 (2013). https://doi.org/10.1007/s00362-011-0421-2

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  • DOI: https://doi.org/10.1007/s00362-011-0421-2

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