IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i19p3474-d923312.html
   My bibliography  Save this article

A New Series Representation and the Laplace Transform for the Lognormal Distribution

Author

Listed:
  • Manuel D. Ortigueira

    (Centre of Technology and Systems—UNINOVA and Department of Electrical Engineering, NOVA School of Science and Technology of NOVA University of Lisbon, Quinta da Torre, 2829-516 Caparica, Portugal)

Abstract

In this paper, the lognormal distribution is studied, and a new series representation is proposed. This series uses the powers of the bilinear function. From it, a simplified form is obtained and used to compute the Laplace transform of the distribution.

Suggested Citation

  • Manuel D. Ortigueira, 2022. "A New Series Representation and the Laplace Transform for the Lognormal Distribution," Mathematics, MDPI, vol. 10(19), pages 1-13, September.
  • Handle: RePEc:gam:jmathe:v:10:y:2022:i:19:p:3474-:d:923312
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/19/3474/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/10/19/3474/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Manuel Duarte Ortigueira & José Tenreiro Machado, 2020. "Revisiting the 1D and 2D Laplace Transforms," Mathematics, MDPI, vol. 8(8), pages 1-24, August.
    2. Søren Asmussen & Jens Ledet Jensen & Leonardo Rojas-Nandayapa, 2016. "On the Laplace Transform of the Lognormal Distribution," Methodology and Computing in Applied Probability, Springer, vol. 18(2), pages 441-458, June.
    3. Khristo N. Boyadzhiev, 2005. "A series transformation formula and related polynomials," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2005, pages 1-18, January.
    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. Christopher Dobronyi & Christian Gouri'eroux, 2020. "Consumer Theory with Non-Parametric Taste Uncertainty and Individual Heterogeneity," Papers 2010.13937, arXiv.org, revised Jan 2021.
    2. Azar, Macarena & Carrasco, Rodrigo A. & Mondschein, Susana, 2022. "Dealing with uncertain surgery times in operating room scheduling," European Journal of Operational Research, Elsevier, vol. 299(1), pages 377-394.
    3. Sunil Kumar Sharma & Waseem A. Khan & Cheon Seoung Ryoo, 2020. "A Parametric Kind of Fubini Polynomials of a Complex Variable," Mathematics, MDPI, vol. 8(4), pages 1-16, April.
    4. Claire Mouminoux & Christophe Dutang & Stéphane Loisel & Hansjoerg Albrecher, 2022. "On a Markovian Game Model for Competitive Insurance Pricing," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 1061-1091, June.
    5. McFadden, Daniel, 2022. "Instability in mixed logit demand models," Journal of choice modelling, Elsevier, vol. 43(C).
    6. Hacène Belbachir & Yahia Djemmada, 2020. "Generalized Geometric Polynomials Via Steffensen’s Generalized Factorials and Tanny’s Operators," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(4), pages 1713-1727, December.
    7. Zied Chaieb & Djibril Gueye, 2022. "Pricing zero-coupon CAT bonds using the enlargement of ltration theory: a general framework ," Post-Print hal-03745077, HAL.
    8. Ruibo Zhang & Daniel Nolte & Cesar Sanchez-Villalobos & Souparno Ghosh & Ranadip Pal, 2024. "Topological regression as an interpretable and efficient tool for quantitative structure-activity relationship modeling," Nature Communications, Nature, vol. 15(1), pages 1-13, December.
    9. Zied Chaieb & Djibril Gueye, 2022. "Pricing zero-coupon CAT bonds using the enlargement of ltration theory: a general framework," Papers 2208.02609, arXiv.org.
    10. Laurence Carassus & Massinissa Ferhoune, 2021. "Efficient approximations for utility-based pricing," Papers 2105.08804, arXiv.org, revised Feb 2024.
    11. Khristo N. Boyadzhiev, 2011. "Series transformation formulas of Euler type, Hadamard product of series, and harmonic number identities," Indian Journal of Pure and Applied Mathematics, Springer, vol. 42(5), pages 371-386, October.
    12. Furman, Edward & Hackmann, Daniel & Kuznetsov, Alexey, 2020. "On log-normal convolutions: An analytical–numerical method with applications to economic capital determination," Insurance: Mathematics and Economics, Elsevier, vol. 90(C), pages 120-134.
    13. Lorenzo Cappello & Stephen G. Walker, 2018. "A Bayesian Motivated Laplace Inversion for Multivariate Probability Distributions," Methodology and Computing in Applied Probability, Springer, vol. 20(2), pages 777-797, June.
    14. Manuel D. Ortigueira, 2022. "A New Look at the Initial Condition Problem," Mathematics, MDPI, vol. 10(10), pages 1-17, May.
    15. 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).
    16. Sunil Kumar Sharma & Waseem Ahmad Khan & Cheon-Seoung Ryoo & Ugur Duran, 2022. "Diverse Properties and Approximate Roots for a Novel Kinds of the ( p , q )-Cosine and ( p , q )-Sine Geometric Polynomials," Mathematics, MDPI, vol. 10(15), pages 1-18, July.
    17. Duarte Valério & Manuel D. Ortigueira & António M. Lopes, 2022. "How Many Fractional Derivatives Are There?," Mathematics, MDPI, vol. 10(5), pages 1-18, February.
    18. António M. Lopes & J. A. Tenreiro Machado, 2022. "Nonlinear Dynamics," Mathematics, MDPI, vol. 10(15), pages 1-3, July.
    19. Müfit Şan & Manuel D. Ortigueira, 2022. "Unilateral Laplace Transforms on Time Scales," Mathematics, MDPI, vol. 10(23), pages 1-21, 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:gam:jmathe:v:10:y:2022:i:19:p:3474-:d:923312. 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.