IDEAS home Printed from https://ideas.repec.org/a/spr/waterr/v36y2022i4d10.1007_s11269-021-03016-w.html
   My bibliography  Save this article

A New Estimation Method for Copula Parameters for Multivariate Hydrological Frequency Analysis With Small Sample Sizes

Author

Listed:
  • Longxia Qian

    (Nanjing University of Posts and Telecommunications
    State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, China Institute of Water Resources and Hydropower Research)

  • Yong Zhao

    (State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, China Institute of Water Resources and Hydropower Research)

  • Jianhong Yang

    (Water resources and reservoir dispatching center of Shaanxi Province)

  • Hanlin Li

    (Nanjing University of Posts and Telecommunications)

  • Hongrui Wang

    (Beijing Normal University)

  • ChengZu Bai

    (Beijing Institute of Applied Meteorology)

Abstract

Multivariate hydrological frequency analysis is important when designing hydraulic and civil infrastructures. However, hydrologic data scarcity and insufficiency are common. By studying the relationship between copula entropy and total correlation estimated by the matrix-based Renyi's α-order entropy functional, a new estimation method (total correlation estimation, TCE) for parameters of the Gumbel-Hougaard copula and Clayton copula was proposed when the sample size was equal to or less than 30. A total of 11,802 simulations were performed to evaluate the performance of TCE for sample sizes ranging from 30 to 5, and were compared with traditional estimation methods that require a large amount of data. As for the Gumbel-Hougaard copula, the performance of TCE is satisfactory regardless of sample size, while the traditional methods perform poorly when the sample size is equal to or less than 20. For the Clayton copula, TCE is reliable and robust and performs well if the sample size is greater than 10, while the traditional methods are unreliable when the sample size is less than 25. Also, TCE is applied to construct the joint distributions of annual runoff and sediment discharge in the Xiliugou River, China. The method based on Renyi's α-order entropy functional provides a new way for multivariate hydrological frequency analysis with small sample sizes.

Suggested Citation

  • Longxia Qian & Yong Zhao & Jianhong Yang & Hanlin Li & Hongrui Wang & ChengZu Bai, 2022. "A New Estimation Method for Copula Parameters for Multivariate Hydrological Frequency Analysis With Small Sample Sizes," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 36(4), pages 1141-1157, March.
    • Handle: RePEc:spr:waterr:v:36:y:2022:i:4:d:10.1007_s11269-021-03016-w
    DOI: 10.1007/s11269-021-03016-w
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11269-021-03016-w
    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/s11269-021-03016-w?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. Fawad, Muhammad & Yan, Ting & Chen, Lu & Huang, Kangdi & Singh, Vijay P., 2019. "Multiparameter probability distributions for at-site frequency analysis of annual maximum wind speed with L-Moments for parameter estimation," Energy, Elsevier, vol. 181(C), pages 724-737.
    2. Wu Zening & He Chentao & Huiliang Wang & Qian Zhang, 2020. "Reservoir Inflow Synchronization Analysis for Four Reservoirs on a Mainstream and its Tributaries in Flood Season Based on a Multivariate Copula Model," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 34(9), pages 2753-2770, July.
    3. Ming Zhong & Ting Zeng & Tao Jiang & Huan Wu & Xiaohong Chen & Yang Hong, 2021. "A Copula-Based Multivariate Probability Analysis for Flash Flood Risk under the Compound Effect of Soil Moisture and Rainfall," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 35(1), pages 83-98, January.
    4. Mohit Prakash Mohanty & Mazhuvanchery Avarachen Sherly & Subhankar Karmakar & Subimal Ghosh, 2018. "Regionalized Design Rainfall Estimation: an Appraisal of Inundation Mapping for Flood Management Under Data-Scarce Situations," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 32(14), pages 4725-4746, November.
    5. Frahm, Gabriel & Junker, Markus & Schmidt, Rafael, 2005. "Estimating the tail-dependence coefficient: Properties and pitfalls," Insurance: Mathematics and Economics, Elsevier, vol. 37(1), pages 80-100, August.
    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. Hanlin Li & Longxia Qian & Jianhong Yang & Suzhen Dang & Mei Hong, 2023. "Parameter Estimation for Univariate Hydrological Distribution Using Improved Bootstrap with Small Samples," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 37(3), pages 1055-1082, February.

    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. Chen An & Ming Dou & Jianling Zhang & Guiqiu Li, 2021. "Method for Analyzing Copula-Based Water Shortage Risk in Multisource Water Supply Cities," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 35(14), pages 4877-4894, November.
    2. Gijbels, Irène & Sznajder, Dominik, 2013. "Testing tail monotonicity by constrained copula estimation," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 338-351.
    3. Ziqiang Xing & Denghua Yan & Cheng Zhang & Gang Wang & Dongdong Zhang, 2015. "Spatial Characterization and Bivariate Frequency Analysis of Precipitation and Runoff in the Upper Huai River Basin, China," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 29(9), pages 3291-3304, July.
    4. Mohamad Haytham Klaho & Hamid R. Safavi & Mohammad H. Golmohammadi & Maamoun Alkntar, 2022. "Comparison between bivariate and trivariate flood frequency analysis using the Archimedean copula functions, a case study of the Karun River in Iran," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 112(2), pages 1589-1610, June.
    5. César Garcia-Gomez & Ana Pérez & Mercedes Prieto-Alaiz, 2022. "The evolution of poverty in the EU-28: a further look based on multivariate tail dependence," Working Papers 605, ECINEQ, Society for the Study of Economic Inequality.
    6. Wenlin Yuan & Lu Lu & Hanzhen Song & Xiang Zhang & Linjuan Xu & Chengguo Su & Meiqi Liu & Denghua Yan & Zening Wu, 2022. "Study on the Early Warning for Flash Flood Based on Random Rainfall Pattern," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 36(5), pages 1587-1609, March.
    7. Tjøstheim, Dag & Hufthammer, Karl Ove, 2013. "Local Gaussian correlation: A new measure of dependence," Journal of Econometrics, Elsevier, vol. 172(1), pages 33-48.
    8. Raza, Hamid & Wu, Weiou, 2018. "Quantile dependence between the stock, bond and foreign exchange markets – Evidence from the UK," The Quarterly Review of Economics and Finance, Elsevier, vol. 69(C), pages 286-296.
    9. Víctor Adame-García & Fernando Fernández-Rodríguez & Simón Sosvilla-Rivero, 2017. "“Resolution of optimization problems and construction of efficient portfolios: An application to the Euro Stoxx 50 index"," IREA Working Papers 201702, University of Barcelona, Research Institute of Applied Economics, revised Feb 2017.
    10. Lamneithem Hangshing & Parmendra P. Dabral, 2018. "Multivariate Frequency Analysis of Meteorological Drought Using Copula," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 32(5), pages 1741-1758, March.
    11. Samiran Das, 2020. "Assessing the Regional Concept with Sub-Sampling Approach to Identify Probability Distribution for at-Site Hydrological Frequency Analysis," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 34(2), pages 803-817, January.
    12. Mendes, Beatriz Vaz de Melo & Arslan, Olcay, 2006. "Multivariate Skew Distributions Based on the GT-Copula," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 26(2), November.
    13. Cerrato, Mario & Crosby, John & Kim, Minjoo & Zhao, Yang, 2015. "US Monetary and Fiscal Policies - Conflict or Cooperation?," SIRE Discussion Papers 2015-78, Scottish Institute for Research in Economics (SIRE).
    14. Yuri Salazar & Wing Ng, 2015. "Nonparametric estimation of general multivariate tail dependence and applications to financial time series," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 24(1), pages 121-158, March.
    15. Hongshi Xu & Kui Xu & Tianye Wang & Wanjie Xue, 2022. "Investigating Flood Risks of Rainfall and Storm Tides Affected by the Parameter Estimation Coupling Bivariate Statistics and Hydrodynamic Models in the Coastal City," IJERPH, MDPI, vol. 19(19), pages 1-18, October.
    16. DiTraglia, Francis J. & Gerlach, Jeffrey R., 2013. "Portfolio selection: An extreme value approach," Journal of Banking & Finance, Elsevier, vol. 37(2), pages 305-323.
    17. Dominique Guégan & Matteo Iacopini, 2018. "Nonparameteric forecasting of multivariate probability density functions," Documents de travail du Centre d'Economie de la Sorbonne 18012, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    18. Pavel Krupskii & Harry Joe, 2015. "Tail-weighted measures of dependence," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(3), pages 614-629, March.
    19. Helena Ferreira & Marta Ferreira, 2021. "Tail dependence and smoothness of time series," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 198-210, March.
    20. Mike So & Alex Tse, 2009. "Dynamic Modeling of Tail Risk: Applications to China, Hong Kong and Other Asian Markets," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 16(3), pages 183-210, September.

    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:waterr:v:36:y:2022:i:4:d:10.1007_s11269-021-03016-w. 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.