IDEAS home Printed from https://ideas.repec.org/p/cte/wsrepe/9864.html
   My bibliography  Save this paper

Characterizations involving conditional expectations based on a functional derivative approach

Author

Listed:
  • Martín, Miguel

Abstract

We introduce a notion of the derivative with respect to a distribution function, not relating necessarily to probability, which generalizes the concept of the derivative as proposed by Lebesgue (1973). The differential calculus required to solve the linear differential equation involved in this notion of the derivative is included in the paper. The definition given here may also be considered as the inverse operator of a modified notion of the Riemmann--Stieltjes integral. Both this unified approach and the results of differential calculus allow us to characterize distributions in terms of three different types of conditional expectations. In applying these results, a test of goodness-of-fit is also indicated. Finally, two characterizations of a general Poisson process are included, based on conditional expectations. Specifically, a useful result for the homogeneous Poisson process is generalized to a general context.

Suggested Citation

  • 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.
  • Handle: RePEc:cte:wsrepe:9864
    as

    Download full text from publisher

    File URL: https://e-archivo.uc3m.es/rest/api/core/bitstreams/16a840ea-e7c3-4a93-9e1c-33df1f0514b4/content
    Download Restriction: no
    ---><---

    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.
    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. 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.
    2. repec:cte:wsrepe:9859 is not listed on IDEAS
    3. 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.
    4. repec:cte:wsrepe:9857 is not listed on IDEAS
    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. 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.

    More about this item

    Keywords

    Characterization results;

    Statistics

    Access and download statistics

    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:cte:wsrepe:9864. 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: Ana Poveda (email available below). General contact details of provider: http://portal.uc3m.es/portal/page/portal/dpto_estadistica .

    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.