IDEAS home Printed from https://ideas.repec.org/a/spr/metrik/v77y2014i3p377-387.html
   My bibliography  Save this article

A new sufficient condition for identifiability of countably infinite mixtures

Author

Listed:
  • Lei Yang
  • Xianyi Wu

Abstract

While identifiability of finite mixtures for a wide range of distributions has been studied by statisticians for decades, discussion on countably infinite mixtures is still limited. This article provides an sufficient condition by means of well-ordered sets and uniform convergence of series. It is then applied to revisit some examples for which the identifiability is well established and then explore the identifiability for several distribution families, including normal, gamma, Cauchy, noncentral $$\chi ^2$$ χ 2 , multivariate normal distributions. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Lei Yang & Xianyi Wu, 2014. "A new sufficient condition for identifiability of countably infinite mixtures," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(3), pages 377-387, April.
    • Handle: RePEc:spr:metrik:v:77:y:2014:i:3:p:377-387
    DOI: 10.1007/s00184-013-0444-x
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00184-013-0444-x
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00184-013-0444-x?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. Wu, Xianyi & Zhou, Xian, 2006. "A new characterization of distortion premiums via countable additivity for comonotonic risks," Insurance: Mathematics and Economics, Elsevier, vol. 38(2), pages 324-334, April.
    2. N. Atienza & J. Garcia-Heras & J. Muñoz-Pichardo, 2006. "A new condition for identifiability of finite mixture distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 63(2), pages 215-221, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Redivo, Edoardo & Nguyen, Hien D. & Gupta, Mayetri, 2020. "Bayesian clustering of skewed and multimodal data using geometric skewed normal distributions," Computational Statistics & Data Analysis, Elsevier, vol. 152(C).

    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. Boonen, Tim J. & Tan, Ken Seng & Zhuang, Sheng Chao, 2016. "The role of a representative reinsurer in optimal reinsurance," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 196-204.
    2. Wei Wang & Limin Wen & Zhixin Yang & Quan Yuan, 2020. "Quantile Credibility Models with Common Effects," Risks, MDPI, vol. 8(4), pages 1-10, September.
    3. Belles-Sampera, Jaume & Merigó, José M. & Guillén, Montserrat & Santolino, Miguel, 2013. "The connection between distortion risk measures and ordered weighted averaging operators," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 411-420.
    4. Gianni Bosi & Magalì Zuanon, 2012. "A note on the axiomatization of Wang premium principle by means of continuity considerations," Economics Bulletin, AccessEcon, vol. 32(4), pages 3158-3165.
    5. Zhang, Jianjun & Qiu, Chunjuan & Wu, Xianyi, 2018. "Bayesian ratemaking with common effects modeled by mixture of Polya tree processes," Insurance: Mathematics and Economics, Elsevier, vol. 82(C), pages 87-94.
    6. Hirbod Assa, 2014. "On Optimal Reinsurance Policy with Distortion Risk Measures and Premiums," Papers 1406.2950, arXiv.org.
    7. Paola Ferretti & Antonella Campana, 2011. "XL reinsurance with reinstatements and initial premium feasibility in exchangeability hypothesis," Working Papers 2011_14, Department of Economics, University of Venice "Ca' Foscari".
    8. Li, Shengguo & Peng, Jin & Zhang, Bo, 2013. "The uncertain premium principle based on the distortion function," Insurance: Mathematics and Economics, Elsevier, vol. 53(2), pages 317-324.
    9. Marta Cardin & Elisa Pagani, 2008. "Some proposals about multivariate risk measurement," Working Papers 165, Department of Applied Mathematics, Università Ca' Foscari Venezia.
    10. Manisera, Marica & Zuccolotto, Paola, 2015. "Identifiability of a model for discrete frequency distributions with a multidimensional parameter space," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 302-316.
    11. Gambacciani, Marco & Paolella, Marc S., 2017. "Robust normal mixtures for financial portfolio allocation," Econometrics and Statistics, Elsevier, vol. 3(C), pages 91-111.
    12. Azari Soufiani, Hossein & Diao, Hansheng & Lai, Zhenyu & Parkes, David C., 2013. "Generalized Random Utility Models with Multiple Types," Scholarly Articles 12363923, Harvard University Department of Economics.
    13. Hirbod Assa, 2015. "Risk management under a prudential policy," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 38(2), pages 217-230, October.
    14. Wen, Limin & Wu, Xianyi & Zhou, Xian, 2009. "The credibility premiums for models with dependence induced by common effects," Insurance: Mathematics and Economics, Elsevier, vol. 44(1), pages 19-25, February.
    15. Cheung, Ka Chun & Yam, Sheung Chi Phillip & Zhang, Yiying, 2019. "Risk-adjusted Bowley reinsurance under distorted probabilities," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 64-72.
    16. Shaoting Li & Jiahua Chen, 2023. "Mixture of shifted binomial distributions for rating data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 75(5), pages 833-853, October.
    17. Assa, Hirbod, 2015. "On optimal reinsurance policy with distortion risk measures and premiums," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 70-75.
    18. Otiniano, C.E.G. & Rathie, P.N. & Ozelim, L.C.S.M., 2015. "On the identifiability of finite mixture of Skew-Normal and Skew-t distributions," Statistics & Probability Letters, Elsevier, vol. 106(C), pages 103-108.

    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:metrik:v:77:y:2014:i:3:p:377-387. 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.