IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v54y2013i1p227-241.html
   My bibliography  Save this article

Identification of power distribution mixtures through regression of exponentials

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00362-011-0421-2
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00362-011-0421-2?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. 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.
    3. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. repec:cte:wsrepe:9857 is not listed on IDEAS
    2. Bobecka, Konstancja & Wesolowski, Jacek, 2004. "Multivariate Lukacs theorem," Journal of Multivariate Analysis, Elsevier, vol. 91(2), pages 143-160, November.
    3. Chou, Chao-Wei & Huang, Wen-Jang, 2004. "On characterizations of the gamma and generalized inverse Gaussian distributions," Statistics & Probability Letters, Elsevier, vol. 69(4), pages 381-388, October.
    4. Martín, Miguel, 2000. "Characterizations involving conditional expectations based on a functional derivative approach," DES - Working Papers. Statistics and Econometrics. WS 9864, Universidad Carlos III de Madrid. Departamento de Estadística.
    5. Lillo, Rosa E., 2004. "On the characterizing property of the convex conditional mean function," Statistics & Probability Letters, Elsevier, vol. 66(1), pages 19-24, January.
    6. 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.
    7. repec:cte:wsrepe:9859 is not listed on IDEAS
    8. Arjun Gupta & Jacek Wesoŀowski, 1999. "Discrete uniform mixtures via posterior means," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 8(2), pages 399-409, December.
    9. Papageorgiou, H. & Wesolowski, Jacek, 1997. "Posterior mean identifies the prior distribution in nb and related models," Statistics & Probability Letters, Elsevier, vol. 36(2), pages 127-134, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:stpapr:v:54:y:2013:i:1:p:227-241. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.