IDEAS home Printed from https://ideas.repec.org/a/wly/envmet/v33y2022i6ne2744.html
   My bibliography  Save this article

A flexible extended generalized Pareto distribution for tail estimation

Author

Listed:
  • Philémon Gamet
  • Jonathan Jalbert

Abstract

For both financial and environmental applications, tail distributions often correspond to extreme risks and an accurate modeling is mandatory. The peaks‐over‐threshold model is a classic way to model the exceedances over a high threshold with the generalized Pareto distribution. However, for some applications, the choice of a high threshold is challenging and the asymptotic conditions for using this model are not always satisfied. The class of extended generalized Pareto models can be used in this case. However, the existing extended model have either infinite or null density at the threshold, which is not consistent with tail modeling. In the present article, we propose new extensions of the generalized Pareto distribution for which the density at the threshold is positive and finite. The proposed extensions provide better estimate of the upper tail index for low thresholds than existing models. They are also appropriate for high thresholds because in that case, the extended models simplify to the generalize Pareto model. The performance and flexibility of the models are illustrated with the modeling of temperature exceeding a low threshold and non‐zero precipitations recorded in Montreal. For non‐zero precipitation, the very low threshold of 0 is used.

Suggested Citation

  • Philémon Gamet & Jonathan Jalbert, 2022. "A flexible extended generalized Pareto distribution for tail estimation," Environmetrics, John Wiley & Sons, Ltd., vol. 33(6), September.
    • Handle: RePEc:wly:envmet:v:33:y:2022:i:6:n:e2744
    DOI: 10.1002/env.2744
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/env.2744
    Download Restriction: no
    File URL: https://libkey.io/10.1002/env.2744?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
    ---><---

    References listed on IDEAS

    as
    1. P. Tencaliec & A.‐C. Favre & P. Naveau & C. Prieur & G. Nicolet, 2020. "Flexible semiparametric generalized Pareto modeling of the entire range of rainfall amount," Environmetrics, John Wiley & Sons, Ltd., vol. 31(2), March.
    2. M. L. Stein, 2017. "Should annual maximum temperatures follow a generalized extreme value distribution?," Biometrika, Biometrika Trust, vol. 104(1), pages 1-16.
    3. M. Carvalho & S. Pereira & P. Pereira & P. Zea Bermudez, 2022. "An Extreme Value Bayesian Lasso for the Conditional Left and Right Tails," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 27(2), pages 222-239, June.
    4. MacDonald, A. & Scarrott, C.J. & Lee, D. & Darlow, B. & Reale, M. & Russell, G., 2011. "A flexible extreme value mixture model," Computational Statistics & Data Analysis, Elsevier, vol. 55(6), pages 2137-2157, June.
    5. Michael L. Stein, 2021. "A parametric model for distributions with flexible behaviour in both tails," Environmetrics, John Wiley & Sons, Ltd., vol. 32(8), December.
    6. Michael L. Stein, 2021. "A parametric model for distributions with flexible behavior in both tails," Environmetrics, John Wiley & Sons, Ltd., vol. 32(2), March.
    7. Rishikesh Yadav & Raphaël Huser & Thomas Opitz, 2021. "Spatial hierarchical modeling of threshold exceedances using rate mixtures," Environmetrics, John Wiley & Sons, Ltd., vol. 32(3), May.
    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. Wilson Gyasi & Kahadawala Cooray, 2024. "New generalized extreme value distribution with applications to extreme temperature data," Environmetrics, John Wiley & Sons, Ltd., vol. 35(3), May.
    2. Sweta Rai & Alexis Hoffman & Soumendra Lahiri & Douglas W. Nychka & Stephan R. Sain & Soutir Bandyopadhyay, 2024. "Fast parameter estimation of generalized extreme value distribution using neural networks," Environmetrics, John Wiley & Sons, Ltd., vol. 35(3), May.

    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. André, L.M. & Wadsworth, J.L. & O'Hagan, A., 2024. "Joint modelling of the body and tail of bivariate data," Computational Statistics & Data Analysis, Elsevier, vol. 189(C).
    2. M. Carvalho & S. Pereira & P. Pereira & P. Zea Bermudez, 2022. "An Extreme Value Bayesian Lasso for the Conditional Left and Right Tails," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 27(2), pages 222-239, June.
    3. Julie Bessac & Robert Underwood & Sheng Di, 2023. "Discussion on “Saving Storage in Climate Ensembles: A Model-Based Stochastic Approach”," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 28(2), pages 358-364, June.
    4. Antonello Maruotti & Pierfrancesco Alaimo Di Loro, 2023. "CO2 emissions and growth: A bivariate bidimensional mean‐variance random effects model," Environmetrics, John Wiley & Sons, Ltd., vol. 34(5), August.
    5. Silius M. Vandeskog & Thordis L. Thorarinsdottir & Ingelin Steinsland & Finn Lindgren, 2022. "Quantile based modeling of diurnal temperature range with the five‐parameter lambda distribution," Environmetrics, John Wiley & Sons, Ltd., vol. 33(4), June.
    6. Fátima Brilhante, M. & Ivette Gomes, M. & Pestana, Dinis, 2013. "A simple generalisation of the Hill estimator," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 518-535.
    7. D. J. Rasmussen & Scott Kulp & Robert E. Kopp & Michael Oppenheimer & Benjamin H. Strauss, 2022. "Popular extreme sea level metrics can better communicate impacts," Climatic Change, Springer, vol. 170(3), pages 1-17, February.
    8. Gloria Buriticá & Philippe Naveau, 2023. "Stable sums to infer high return levels of multivariate rainfall time series," Environmetrics, John Wiley & Sons, Ltd., vol. 34(4), June.
    9. Chunli Huang & Xu Zhao & Weihu Cheng & Qingqing Ji & Qiao Duan & Yufei Han, 2022. "Statistical Inference of Dynamic Conditional Generalized Pareto Distribution with Weather and Air Quality Factors," Mathematics, MDPI, vol. 10(9), pages 1-25, April.
    10. Cristiano Villa, 2017. "Bayesian estimation of the threshold of a generalised pareto distribution for heavy-tailed observations," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(1), pages 95-118, March.
    11. Chiara Lattanzi & Manuele Leonelli, 2019. "A changepoint approach for the identification of financial extreme regimes," Papers 1902.09205, arXiv.org.
    12. Juan Gonzalez & Daniela Rodriguez & Mariela Sued, 2013. "Threshold selection for extremes under a semiparametric model," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 22(4), pages 481-500, November.
    13. Schaumburg, Julia, 2012. "Predicting extreme value at risk: Nonparametric quantile regression with refinements from extreme value theory," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4081-4096.
    14. Toumi, Kaouther & Viviani, Jean-Laurent & Chayeh, Zeinab, 2019. "Measurement of the displaced commercial risk in Islamic Banks," The Quarterly Review of Economics and Finance, Elsevier, vol. 74(C), pages 18-31.
    15. Kangyi Li & Yang Zhou, 2024. "Improved Financial Predicting Method Based on Time Series Long Short-Term Memory Algorithm," Mathematics, MDPI, vol. 12(7), pages 1-17, April.
    16. Sigauke, Caston & Verster, Andréhette & Chikobvu, Delson, 2013. "Extreme daily increases in peak electricity demand: Tail-quantile estimation," Energy Policy, Elsevier, vol. 53(C), pages 90-96.
    17. So, Mike K.P. & Chan, Raymond K.S., 2014. "Bayesian analysis of tail asymmetry based on a threshold extreme value model," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 568-587.
    18. Wendy Shinyie & Noriszura Ismail & Abdul Jemain, 2014. "Semi-parametric Estimation Based on Second Order Parameter for Selecting Optimal Threshold of Extreme Rainfall Events," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 28(11), pages 3489-3514, September.
    19. Federica Stolf & Antonio Canale, 2023. "A hierarchical Bayesian non‐asymptotic extreme value model for spatial data," Environmetrics, John Wiley & Sons, Ltd., vol. 34(7), November.
    20. Dacorogna, Michel & Debbabi, Nehla & Kratz, Marie, 2023. "Building up cyber resilience by better grasping cyber risk via a new algorithm for modelling heavy-tailed data," European Journal of Operational Research, Elsevier, vol. 311(2), pages 708-729.

    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:wly:envmet:v:33:y:2022:i:6:n:e2744. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.interscience.wiley.com/jpages/1180-4009/ .

    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.