IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i7p1758-d1117696.html
   My bibliography  Save this article

Modelling Heavy Tailed Phenomena Using a LogNormal Distribution Having a Numerically Verifiable Infinite Variance

Author

Listed:
  • Marco Cococcioni

    (Department of Information Engineering, L.go Lucio Lazzarino, 1-56122 Pisa, Italy
    These authors contributed equally to this work.)

  • Francesco Fiorini

    (Department of Information Engineering, L.go Lucio Lazzarino, 1-56122 Pisa, Italy
    These authors contributed equally to this work.)

  • Michele Pagano

    (Department of Information Engineering, L.go Lucio Lazzarino, 1-56122 Pisa, Italy
    These authors contributed equally to this work.)

Abstract

One-sided heavy tailed distributions have been used in many engineering applications, ranging from teletraffic modelling to financial engineering. In practice, the most interesting heavy tailed distributions are those having a finite mean and a diverging variance. The LogNormal distribution is sometimes discarded from modelling heavy tailed phenomena because it has a finite variance, even when it seems the most appropriate one to fit the data. In this work we provide for the first time a LogNormal distribution having a finite mean and a variance which converges to a well-defined infinite value. This is possible thanks to the use of Non-Standard Analysis. In particular, we have been able to obtain a Non-Standard LogNormal distribution, for which it is possible to numerically and experimentally verify whether the expected mean and variance of a set of generated pseudo-random numbers agree with the theoretical ones. Moreover, such a check would be much more cumbersome (and sometimes even impossible) when considering heavy tailed distributions in the traditional framework of standard analysis.

Suggested Citation

  • Marco Cococcioni & Francesco Fiorini & Michele Pagano, 2023. "Modelling Heavy Tailed Phenomena Using a LogNormal Distribution Having a Numerically Verifiable Infinite Variance," Mathematics, MDPI, vol. 11(7), pages 1-16, April.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:7:p:1758-:d:1117696
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/7/1758/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/7/1758/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Michele Leonardo Bianchi & Stoyan V Stoyanov & Gian Luca Tassinari & Frank J Fabozzi & Sergio M Focardi, 2019. "Handbook of Heavy-Tailed Distributions in Asset Management and Risk Management," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 11118, December.
    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. Karol I. Santoro & Diego I. Gallardo & Osvaldo Venegas & Isaac E. Cortés & Héctor W. Gómez, 2023. "A Heavy-Tailed Distribution Based on the Lomax–Rayleigh Distribution with Applications to Medical Data," Mathematics, MDPI, vol. 11(22), pages 1-15, November.

    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. Wang, Xuqin & Li, Muyi, 2023. "Bootstrapping the transformed goodness-of-fit test on heavy-tailed GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 184(C).
    2. Massimo Arnone & Michele Leonardo Bianchi & Anna Grazia Quaranta & Gian Luca Tassinari, 2021. "Catastrophic risks and the pricing of catastrophe equity put options," Computational Management Science, Springer, vol. 18(2), pages 213-237, June.
    3. Michele Leonardo Bianchi & Asmerilda Hitaj & Gian Luca Tassinari, 2020. "Multivariate non-Gaussian models for financial applications," Papers 2005.06390, arXiv.org.
    4. José Antonio Climent Hernández & Gabino Sánchez Arzate & Ambrosio Ortiz Ramírez, 2021. "Portafolios ?-estables del G20: Evidencia empírica con Markowitz, Tobin y CAPM," Remef - Revista Mexicana de Economía y Finanzas Nueva Época REMEF (The Mexican Journal of Economics and Finance), Instituto Mexicano de Ejecutivos de Finanzas, IMEF, vol. 16(4), pages 1-28, Octubre -.
    5. Michele Leonardo Bianchi & Alberto Maria Sorrentino, 2020. "Measuring CoVaR: An Empirical Comparison," Computational Economics, Springer;Society for Computational Economics, vol. 55(2), pages 511-528, February.
    6. Michele Leonardo Bianchi, 2023. "Assessing and forecasting the market risk of bank securities holdings: a data-driven approach," Risk Management, Palgrave Macmillan, vol. 25(4), pages 1-23, December.
    7. Zaevski, Tsvetelin S. & Nedeltchev, Dragomir C., 2023. "From BASEL III to BASEL IV and beyond: Expected shortfall and expectile risk measures," International Review of Financial Analysis, Elsevier, vol. 87(C).
    8. Bianchi, Michele Leonardo & De Luca, Giovanni & Rivieccio, Giorgia, 2023. "Non-Gaussian models for CoVaR estimation," International Journal of Forecasting, Elsevier, vol. 39(1), pages 391-404.
    9. Michele Leonardo Bianchi & Giovanni De Luca & Giorgia Rivieccio, 2020. "CoVaR with volatility clustering, heavy tails and non-linear dependence," Papers 2009.10764, arXiv.org.

    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:gam:jmathe:v:11:y:2023:i:7:p:1758-:d:1117696. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.