IDEAS home Printed from https://ideas.repec.org/a/spr/metrik/v88y2025i1d10.1007_s00184-024-00947-3.html
   My bibliography  Save this article

Stochastic comparisons, differential entropy and varentropy for distributions induced by probability density functions

Author

Listed:
  • Antonio Di Crescenzo

    (Università degli Studi di Salerno)

  • Luca Paolillo

    (Università degli Studi di Salerno)

  • Alfonso Suárez-Llorens

    (Universidad de Cádiz)

Abstract

Stimulated by the need of describing useful notions related to information measures, we introduce the ‘pdf-related distributions’. These are defined in terms of transformation of absolutely continuous random variables through their own probability density functions. We investigate their main characteristics, with reference to the general form of the distribution, the quantiles, and some related notions of reliability theory. This allows us to obtain a characterization of the pdf-related distribution being uniform for distributions of exponential and Laplace type as well. We also face the problem of stochastic comparing the pdf-related distributions by resorting to suitable stochastic orders. Finally, the given results are used to analyse properties and to compare some useful information measures, such as the differential entropy and the varentropy.

Suggested Citation

  • Antonio Di Crescenzo & Luca Paolillo & Alfonso Suárez-Llorens, 2025. "Stochastic comparisons, differential entropy and varentropy for distributions induced by probability density functions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 88(1), pages 43-59, January.
    • Handle: RePEc:spr:metrik:v:88:y:2025:i:1:d:10.1007_s00184-024-00947-3
    DOI: 10.1007/s00184-024-00947-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00184-024-00947-3
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00184-024-00947-3?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.

    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:88:y:2025:i:1:d:10.1007_s00184-024-00947-3. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.