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Parameter Estimation for Univariate Hydrological Distribution Using Improved Bootstrap with Small Samples

Author

Listed:
  • Hanlin Li

    (Nanjing University of Posts and Telecommunications)

  • Longxia Qian

    (Nanjing University of Posts and Telecommunications
    Nanjing Hydraulic Research Institute)

  • Jianhong Yang

    (Water Resources and Reservoir Dispatching Center of Shanxi Province)

  • Suzhen Dang

    (Yellow River Institute of Hydraulic Research, Yellow River Conservancy Commission)

  • Mei Hong

    (National University of Defense Technology)

Abstract

It is crucial yet challenging to estimate the parameters of hydrological distribution for hydrological frequency analysis when small samples are available. This paper proposes an improved Bootstrap and combines it with three commonly used parameter estimation methods, i.e., improved Bootstrap with method of moments (IBMOM), maximum likelihood estimation (IBMLE) and maximum entropy principle (IBMEP). A series of numerical experiments with different small sized (10, 20, and 30) of samples generated from the three commonly used probability distributions, i.e., Pearson Type III, Weibull, and Beta distributions, are conducted to evaluate the performance of the proposed three methods compared with the cases of conventional Bootstrap and without-Bootstrap. The proposed methods are then applied to the estimation of distribution parameters for the average annual precipitations of 8 counties in Qingyang City, China with assumption of Pearson Type III distribution for the average annual precipitations. The resulting absolute deviation (AD) box plots and Root Mean Square Error (RMSE) and bias estimators from both the numerical experiments and the case study show that the estimated parameters obtained by the improved Bootstrap methods have less deviation and are more accurate than those obtained through conventional Bootstrap and without-Bootstrap for the three distributions. It is also interestingly found that the improved Bootstrap provides more relative improvement on the parameter estimation when smaller size of sample is used. The method based on improved Bootstrap paves a new way forward to alleviating the need of large size of sample for quality hydrological frequency analysis.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:waterr:v:37:y:2023:i:3:d:10.1007_s11269-022-03410-y
    DOI: 10.1007/s11269-022-03410-y
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    References listed on IDEAS

    as
    1. 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.
    2. Guan-Jun Lei & Jun-Xian Yin & Wen-Chuan Wang & Hao Wang, 2018. "The Analysis and Improvement of the Fuzzy Weighted Optimum Curve-Fitting Method of Pearson – Type III Distribution," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 32(14), pages 4511-4526, November.
    3. Muhammad Shafeeq ul Rehman Khan & Zamir Hussain & Ishfaq Ahmad, 2021. "Effects of L-Moments, Maximum Likelihood and Maximum Product of Spacing Estimation Methods in Using Pearson Type-3 Distribution for Modeling Extreme Values," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 35(5), pages 1415-1431, March.
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    Cited by:

    1. Kouao Laurent Kouadio & Jianxin Liu & Serge Kouamelan Kouamelan & Rong Liu, 2023. "Ensemble Learning Paradigms for Flow Rate Prediction Boosting," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 37(11), pages 4413-4431, September.

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