IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v265y2015icp225-236.html
   My bibliography  Save this article

Entropy and density approximation from Laplace transforms

Author

Listed:
  • Gzyl, Henryk
  • Novi Inverardi, Pierluigi
  • Tagliani, Aldo

Abstract

How much information does the Laplace transforms on the real line carry about an unknown, absolutely continuous distribution? If we measure that information by the Boltzmann–Gibbs–Shannon entropy, the original question becomes: How to determine the information in a probability density from the given values of its Laplace transform. We prove that a reliable evaluation both of the entropy and density can be done by exploiting some theoretical results about entropy convergence, that involve only finitely many real values of the Laplace transform, without having to invert the Laplace transform.We provide a bound for the approximation error of in terms of the Kullback–Leibler distance and a method for calculating the density to arbitrary accuracy.

Suggested Citation

  • Gzyl, Henryk & Novi Inverardi, Pierluigi & Tagliani, Aldo, 2015. "Entropy and density approximation from Laplace transforms," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 225-236.
    • Handle: RePEc:eee:apmaco:v:265:y:2015:i:c:p:225-236
    DOI: 10.1016/j.amc.2015.05.020
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300315006372
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2015.05.020?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. Mnatsakanov, Robert M., 2008. "Hausdorff moment problem: Reconstruction of distributions," Statistics & Probability Letters, Elsevier, vol. 78(12), pages 1612-1618, September.
    2. Henryk Gzyl & Pier Luigi Novi Inverardi & Aldo Tagliani, 2014. "Fractional Moments and Maximum Entropy: Geometric Meaning," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 43(17), pages 3596-3601, September.
    3. Mnatsakanov, Robert M., 2008. "Hausdorff moment problem: Reconstruction of probability density functions," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1869-1877, September.
    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. Zhang, Yang & Xu, Jun & Gardoni, Paolo, 2024. "A loading contribution degree analysis-based strategy for time-variant reliability analysis of structures under multiple loading stochastic processes," Reliability Engineering and System Safety, Elsevier, vol. 243(C).
    2. Zhang, Yang & Xu, Jun & Beer, Michael, 2023. "A single-loop time-variant reliability evaluation via a decoupling strategy and probability distribution reconstruction," Reliability Engineering and System Safety, Elsevier, vol. 232(C).
    3. Dang, Chao & Xu, Jun, 2020. "Unified reliability assessment for problems with low- to high-dimensional random inputs using the Laplace transform and a mixture distribution," Reliability Engineering and System Safety, Elsevier, vol. 204(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. Mnatsakanov, Robert M., 2011. "Moment-recovered approximations of multivariate distributions: The Laplace transform inversion," Statistics & Probability Letters, Elsevier, vol. 81(1), pages 1-7, January.
    2. Diel, Roland & Lerasle, Matthieu, 2018. "Non parametric estimation for random walks in random environment," Stochastic Processes and their Applications, Elsevier, vol. 128(1), pages 132-155.
    3. Hansjörg Albrecher & José Carlos Araujo-Acuna, 2022. "On The Randomized Schmitter Problem," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 515-535, June.
    4. Mnatsakanov, Robert M. & Sarkisian, Khachatur & Hakobyan, Artak, 2015. "Approximation of the ruin probability using the scaled Laplace transform inversion," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 717-727.
    5. Mnatsakanov, Robert & Sarkisian, Khachatur, 2012. "Varying kernel density estimation on R+," Statistics & Probability Letters, Elsevier, vol. 82(7), pages 1337-1345.
    6. Gzyl, Henryk & Novi-Inverardi, Pier-Luigi & Tagliani, Aldo, 2013. "Determination of the probability of ultimate ruin by maximum entropy applied to fractional moments," Insurance: Mathematics and Economics, Elsevier, vol. 53(2), pages 457-463.
    7. Calès, Ludovic & Chalkis, Apostolos & Emiris, Ioannis Z., 2019. "On the cross-sectional distribution of portfolio returns," JRC Working Papers in Economics and Finance 2019-11, Joint Research Centre, European Commission.
    8. Mnatsakanov, Robert M., 2008. "Hausdorff moment problem: Reconstruction of probability density functions," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1869-1877, September.
    9. Weimei Li & Leifu Gao, 2024. "Research on Risk-Averse Procurement Optimization of Emergency Supplies for Mine Thermodynamic Disasters," Mathematics, MDPI, vol. 12(14), pages 1-17, July.
    10. Mnatsakanov, Robert M. & Pommeret, Denys, 2024. "On recovering the relative distribution, Part 1: The moment-recovered approach," Statistics & Probability Letters, Elsevier, vol. 208(C).
    11. Mnatsakanov, Robert M. & Li, Shengqiao, 2013. "The Radon transform inversion using moments," Statistics & Probability Letters, Elsevier, vol. 83(3), pages 936-942.
    12. Ludovic Cal`es & Apostolos Chalkis & Ioannis Z. Emiris, 2021. "The cross-sectional distribution of portfolio returns and applications," Papers 2105.06573, arXiv.org.
    13. Robert M. Mnatsakanov & Hansjoerg Albrecher & Stephane Loisel, 2022. "Approximations of Copulas via Transformed Moments," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 3175-3193, 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:eee:apmaco:v:265:y:2015:i:c:p:225-236. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.