IDEAS home Printed from https://ideas.repec.org/a/spr/compst/v37y2022i4d10.1007_s00180-021-01179-z.html
   My bibliography  Save this article

The truncated g-and-h distribution: estimation and application to loss modeling

Author

Listed:
  • Marco Bee

    (University of Trento)

Abstract

The g-and-h distribution is a flexible model for skewed and/or leptokurtic data, which has been shown to be especially effective in actuarial analytics and risk management. Since in these fields data are often recorded only above a certain threshold, we introduce a left-truncated g-and-h distribution. Given the lack of an explicit density, we estimate the parameters via an Approximate Maximum Likelihood approach that uses the empirical characteristic function as summary statistics. Simulation results and an application to fire insurance losses suggest that the method works well and that the explicit consideration of truncation is strongly preferable with respect the use of the non-truncated g-and-h distribution.

Suggested Citation

  • Marco Bee, 2022. "The truncated g-and-h distribution: estimation and application to loss modeling," Computational Statistics, Springer, vol. 37(4), pages 1771-1794, September.
    • Handle: RePEc:spr:compst:v:37:y:2022:i:4:d:10.1007_s00180-021-01179-z
    DOI: 10.1007/s00180-021-01179-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00180-021-01179-z
    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/s00180-021-01179-z?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. Degen, Matthias & Embrechts, Paul & Lambrigger, Dominik D., 2007. "The Quantitative Modeling of Operational Risk: Between G-and-H and EVT," ASTIN Bulletin, Cambridge University Press, vol. 37(2), pages 265-291, November.
    2. M. Bee & J. Hambuckers & L. Trapin, 2019. "Estimating Value-at-Risk for the g-and-h distribution: an indirect inference approach," Quantitative Finance, Taylor & Francis Journals, vol. 19(8), pages 1255-1266, August.
    3. Rene Garcia & Eric Renault & David Veredas, 2011. "Estimation of stable distributions with indirect inference," ULB Institutional Repository 2013/136186, ULB -- Universite Libre de Bruxelles.
    4. Garcia, René & Renault, Eric & Veredas, David, 2011. "Estimation of stable distributions by indirect inference," Journal of Econometrics, Elsevier, vol. 161(2), pages 325-337, April.
    5. Marine Carrasco & Jean-Pierre Florens, 2000. "Efficient GMM Estimation Using the Empirical Characteristic Function," Working Papers 2000-33, Center for Research in Economics and Statistics.
    6. Nadarajah, Saralees & Kotz, Samuel, 2006. "R Programs for Truncated Distributions," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 16(c02).
    7. Gareth W. Peters & Wilson Y. Chen & Richard H. Gerlach, 2016. "Estimating Quantile Families of Loss Distributions for Non-Life Insurance Modelling via L-moments," Papers 1603.01041, arXiv.org.
    8. Alexander J. McNeil & Rüdiger Frey & Paul Embrechts, 2015. "Quantitative Risk Management: Concepts, Techniques and Tools Revised edition," Economics Books, Princeton University Press, edition 2, number 10496.
    9. M. Bee & J. Hambuckers & L. Trapin, 2021. "Estimating large losses in insurance analytics and operational risk using the g-and-h distribution," Quantitative Finance, Taylor & Francis Journals, vol. 21(7), pages 1207-1221, July.
    10. M. Bee & L. Trapin, 2018. "A characteristic function-based approach to approximate maximum likelihood estimation," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(13), pages 3138-3160, July.
    11. Gareth W. Peters & Wilson Ye Chen & Richard H. Gerlach, 2016. "Estimating Quantile Families of Loss Distributions for Non-Life Insurance Modelling via L-Moments," Risks, MDPI, vol. 4(2), pages 1-41, May.
    12. Kabir Dutta & Jason Perry, 2006. "A tale of tails: an empirical analysis of loss distribution models for estimating operational risk capital," Working Papers 06-13, Federal Reserve Bank of Boston.
    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. Marco Bee & Julien Hambuckers & Luca Trapin, 2019. "An improved approach for estimating large losses in insurance analytics and operational risk using the g-and-h distribution," DEM Working Papers 2019/11, Department of Economics and Management.
    2. Marco Bee & Julien Hambuckers & Flavio Santi & Luca Trapin, 2021. "Testing a parameter restriction on the boundary for the g-and-h distribution: a simulated approach," Computational Statistics, Springer, vol. 36(3), pages 2177-2200, September.
    3. M. Bee & J. Hambuckers & L. Trapin, 2019. "Estimating Value-at-Risk for the g-and-h distribution: an indirect inference approach," Quantitative Finance, Taylor & Francis Journals, vol. 19(8), pages 1255-1266, August.
    4. Gareth W. Peters, 2018. "General Quantile Time Series Regressions for Applications in Population Demographics," Risks, MDPI, vol. 6(3), pages 1-47, September.
    5. Gareth W. Peters & Pavel V. Shevchenko & Bertrand K. Hassani & Ariane Chapelle, 2016. "Should the advanced measurement approach be replaced with the standardized measurement approach for operational risk?," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01391091, HAL.
    6. Gareth W. Peters & Wilson Ye Chen & Richard H. Gerlach, 2016. "Estimating Quantile Families of Loss Distributions for Non-Life Insurance Modelling via L-Moments," Risks, MDPI, vol. 4(2), pages 1-41, May.
    7. Gareth W. Peters & Wilson Y. Chen & Richard H. Gerlach, 2016. "Estimating Quantile Families of Loss Distributions for Non-Life Insurance Modelling via L-moments," Papers 1603.01041, arXiv.org.
    8. Gareth W. Peters & Pavel V. Shevchenko & Bertrand Hassani & Ariane Chapelle, 2016. "Should the advanced measurement approach be replaced with the standardized measurement approach for operational risk?," Papers 1607.02319, arXiv.org, revised Sep 2016.
    9. Gareth W. Peters & Pavel V. Shevchenko & Bertrand K. Hassani & Ariane Chapelle, 2016. "Should the advanced measurement approach be replaced with the standardized measurement approach for operational risk?," Post-Print halshs-01391091, HAL.
    10. Wilson Ye Chen & Gareth W. Peters & Richard H. Gerlach & Scott A. Sisson, 2017. "Dynamic Quantile Function Models," Papers 1707.02587, arXiv.org, revised May 2021.
    11. Gareth W. Peters & Pavel V. Shevchenko & Bertrand K. Hassani & Ariane Chapelle, 2016. "Should the advanced measurement approach be replaced with the standardized measurement approach for operational risk?," Documents de travail du Centre d'Economie de la Sorbonne 16065, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    12. Tsionas, Mike, 2012. "Simple techniques for likelihood analysis of univariate and multivariate stable distributions: with extensions to multivariate stochastic volatility and dynamic factor models," MPRA Paper 40966, University Library of Munich, Germany, revised 20 Aug 2012.
    13. Buch-Kromann, Tine & Guillén, Montserrat & Linton, Oliver & Nielsen, Jens Perch, 2011. "Multivariate density estimation using dimension reducing information and tail flattening transformations," Insurance: Mathematics and Economics, Elsevier, vol. 48(1), pages 99-110, January.
    14. Chaussé, Pierre, 2010. "Computing Generalized Method of Moments and Generalized Empirical Likelihood with R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 34(i11).
    15. Dominicy, Yves & Veredas, David, 2013. "The method of simulated quantiles," Journal of Econometrics, Elsevier, vol. 172(2), pages 235-247.
    16. Kotchoni, Rachidi, 2012. "Applications of the characteristic function-based continuum GMM in finance," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3599-3622.
    17. Antonio Díaz & Gonzalo García-Donato & Andrés Mora-Valencia, 2017. "Risk quantification in turmoil markets," Risk Management, Palgrave Macmillan, vol. 19(3), pages 202-224, August.
    18. Garcia, René & Renault, Eric & Veredas, David, 2011. "Estimation of stable distributions by indirect inference," Journal of Econometrics, Elsevier, vol. 161(2), pages 325-337, April.
    19. Calzolari, Giorgio & Halbleib, Roxana & Parrini, Alessandro, 2014. "Estimating GARCH-type models with symmetric stable innovations: Indirect inference versus maximum likelihood," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 158-171.
    20. Marco Bee, 2018. "Estimating the wrapped stable distribution via indirect inference," DEM Working Papers 2018/11, Department of Economics and Management.

    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:compst:v:37:y:2022:i:4:d:10.1007_s00180-021-01179-z. 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: 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.