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Identification of power distribution mixtures through regression of exponentials

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  • Wen-Jang Huang
  • Nan-Cheng Su

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

Suggested Citation

  • Wen-Jang Huang & Nan-Cheng Su, 2013. "Identification of power distribution mixtures through regression of exponentials," Statistical Papers, Springer, vol. 54(1), pages 227-241, February.
    • Handle: RePEc:spr:stpapr:v:54:y:2013:i:1:p:227-241
    DOI: 10.1007/s00362-011-0421-2
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    References listed on IDEAS

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    1. Arjun Gupta & Jacek Wesolowski, 1997. "Uniform Mixtures Via Posterior Means," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 49(1), pages 171-180, March.
    2. Gupta Arjun K. & Wesolowski Jacek, 2001. "Regressional Identifiability And Identification For Beta Mixtures," Statistics & Risk Modeling, De Gruyter, vol. 19(1), pages 71-82, January.
    3. Shun-Hwa Li & Wen-Jang Huang & Mong-Na Huang, 1994. "Characterizations of the Poisson process as a renewal process via two conditional moments," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 46(2), pages 351-360, June.
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