IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2302.02486.html
   My bibliography  Save this paper

The Difference-of-Log-Normals Distribution: Properties, Estimation, and Growth

Author

Listed:
  • Robert Parham

Abstract

This paper describes the Difference-of-Log-Normals (DLN) distribution. A companion paper makes the case that the DLN is a fundamental distribution in nature, and shows how a simple application of the CLT gives rise to the DLN in many disparate phenomena. Here, I characterize its PDF, CDF, moments, and parameter estimators; generalize it to N-dimensions using spherical distribution theory; describe methods to deal with its signature ``double-exponential'' nature; and use it to generalize growth measurement to possibly-negative variates distributing DLN. I also conduct Monte-Carlo experiments to establish some properties of the estimators and measures described.

Suggested Citation

  • Robert Parham, 2023. "The Difference-of-Log-Normals Distribution: Properties, Estimation, and Growth," Papers 2302.02486, arXiv.org.
    • Handle: RePEc:arx:papers:2302.02486
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2302.02486
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Archil Gulisashvili & Peter Tankov, 2013. "Tail behavior of sums and differences of log-normal random variables," Papers 1309.3057, arXiv.org, revised Jan 2016.
    2. Lorentz Jäntschi & Sorana D. Bolboacă, 2018. "Computation of Probability Associated with Anderson–Darling Statistic," Mathematics, MDPI, vol. 6(6), pages 1-17, May.
    3. C. F. Lo, 2012. "The Sum and Difference of Two Lognormal Random Variables," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-13, September.
    4. Marc F. Bellemare & Casey J. Wichman, 2020. "Elasticities and the Inverse Hyperbolic Sine Transformation," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 82(1), pages 50-61, February.
    5. Cambanis, Stamatis & Huang, Steel & Simons, Gordon, 1981. "On the theory of elliptically contoured distributions," Journal of Multivariate Analysis, Elsevier, vol. 11(3), pages 368-385, September.
    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. Leopoldo Fergusson & Carlos Molina, 2020. "Facebook Causes Protests," HiCN Working Papers 323, Households in Conflict Network.
    2. Aksoy, Cevat Giray & Poutvaara, Panu & Schikora, Felicitas, 2023. "First time around: Local conditions and multi-dimensional integration of refugees," Journal of Urban Economics, Elsevier, vol. 137(C).
    3. Giuseppe Maggio & Marina Mastrorillo & Nicholas J. Sitko, 2022. "Adapting to High Temperatures: Effect of Farm Practices and Their Adoption Duration on Total Value of Crop Production in Uganda," American Journal of Agricultural Economics, John Wiley & Sons, vol. 104(1), pages 385-403, January.
    4. Emanuele Amodio & Michele Battisti & Antonio Francesco Gravina & Andrea Mario Lavezzi & Giuseppe Maggio, 2023. "School‐age vaccination, school openings and Covid‐19 diffusion," Health Economics, John Wiley & Sons, Ltd., vol. 32(5), pages 1084-1100, May.
    5. Falk, Michael, 1998. "A Note on the Comedian for Elliptical Distributions," Journal of Multivariate Analysis, Elsevier, vol. 67(2), pages 306-317, November.
    6. La Ferrara, Eliana & Corno, Lucia & Voena, Alessandra, 2020. "Female Genital Cutting and the Slave Trade," CEPR Discussion Papers 15577, C.E.P.R. Discussion Papers.
    7. Kume, Alfred & Hashorva, Enkelejd, 2012. "Calculation of Bayes premium for conditional elliptical risks," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 632-635.
    8. Jacob, P. & Suquet, Ch., 1997. "Regression and asymptotical location of a multivariate sample," Statistics & Probability Letters, Elsevier, vol. 35(2), pages 173-179, September.
    9. Tarpey, Thaddeus, 2000. "Parallel Principal Axes," Journal of Multivariate Analysis, Elsevier, vol. 75(2), pages 295-313, November.
    10. Erik Brynjolfsson & Catherine Buffington & Nathan Goldschlag & J. Frank Li & Javier Miranda & Robert Seamans, 2023. "The Characteristics and Geographic Distribution of Robot Hubs in U.S. Manufacturing Establishments," Working Papers 23-14, Center for Economic Studies, U.S. Census Bureau.
    11. Isaac E. Cortés & Osvaldo Venegas & Héctor W. Gómez, 2022. "A Symmetric/Asymmetric Bimodal Extension Based on the Logistic Distribution: Properties, Simulation and Applications," Mathematics, MDPI, vol. 10(12), pages 1-17, June.
    12. Valdez, Emiliano A. & Chernih, Andrew, 2003. "Wang's capital allocation formula for elliptically contoured distributions," Insurance: Mathematics and Economics, Elsevier, vol. 33(3), pages 517-532, December.
    13. Thomas S. Dee & Emily K. Penner, 2021. "My Brother's Keeper? The Impact of Targeted Educational Supports," Journal of Policy Analysis and Management, John Wiley & Sons, Ltd., vol. 40(4), pages 1171-1196, September.
    14. Preinerstorfer, David & Pötscher, Benedikt M., 2017. "On The Power Of Invariant Tests For Hypotheses On A Covariance Matrix," Econometric Theory, Cambridge University Press, vol. 33(1), pages 1-68, February.
    15. Genthner, Robert & Kis-Katos, Krisztina, 2022. "Foreign investment regulation and firm productivity: Granular evidence from Indonesia," Journal of Comparative Economics, Elsevier, vol. 50(3), pages 668-687.
    16. Patrick Bennett, 2021. "The Work-To-School Transition: Job Displacement and Skill Upgrading among Young High School Dropouts," CESifo Working Paper Series 9417, CESifo.
    17. Stephan Heblich & Stephen J. Redding & Hans-Joachim Voth, 2022. "Slavery and the British Industrial Revolution," CEP Discussion Papers dp1884, Centre for Economic Performance, LSE.
    18. Jiang, Wenhao & Stickley, Andrew & Ueda, Michiko, 2021. "Green space and suicide mortality in Japan: An ecological study," Social Science & Medicine, Elsevier, vol. 282(C).
    19. Peng Ding, 2016. "On the Conditional Distribution of the Multivariate Distribution," The American Statistician, Taylor & Francis Journals, vol. 70(3), pages 293-295, July.
    20. Walelign,Solomon Zena & Wang Sonne,Soazic Elise & Seshan,Ganesh Kumar, 2022. "Livelihood Impacts of Refugees on Host Communities : Evidence from Ethiopia," Policy Research Working Paper Series 10044, The World Bank.

    More about this item

    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:arx:papers:2302.02486. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.