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Estimating precipitation extremes using the log‐histospline

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  • Whitney K. Huang
  • Douglas W. Nychka
  • Hao Zhang

Abstract

One of the commonly used approaches in modeling extremes is the peaks‐over‐threshold (POT) method. The POT method models exceedances over a threshold that is sufficiently high so that the exceedance has approximately a generalized Pareto distribution. This method requires the selection of a threshold that might affect the estimates. Here, we propose an alternative method, the log‐histospline (LHSpline), to explore modeling the tail behavior and the remainder of the density in one step using the full range of the data. LHSpline applies a smoothing spline model to a finely binned histogram of the log‐transformed data to estimate its log density. By construction, a LHSpline estimation is constrained to have polynomial tail behavior, a feature commonly observed in daily rainfall observations. We illustrate the LHSpline method by analyzing precipitation data collected in Houston, Texas.

Suggested Citation

  • Whitney K. Huang & Douglas W. Nychka & Hao Zhang, 2019. "Estimating precipitation extremes using the log‐histospline," Environmetrics, John Wiley & Sons, Ltd., vol. 30(4), June.
    • Handle: RePEc:wly:envmet:v:30:y:2019:i:4:n:e2543
    DOI: 10.1002/env.2543
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    Cited by:

    1. Carlynn Fagnant & Avantika Gori & Antonia Sebastian & Philip B. Bedient & Katherine B. Ensor, 2020. "Characterizing spatiotemporal trends in extreme precipitation in Southeast Texas," 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. 104(2), pages 1597-1621, November.
    2. Brook T. Russell & Whitney K. Huang, 2021. "Modeling short‐ranged dependence in block extrema with application to polar temperature data," Environmetrics, John Wiley & Sons, Ltd., vol. 32(3), May.
    3. Chang Yu & Ondrej Blaha & Michael Kane & Wei Wei & Denise Esserman & Daniel Zelterman, 2022. "Regression methods for the appearances of extremes in climate data," Environmetrics, John Wiley & Sons, Ltd., vol. 33(7), November.
    4. 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).
    5. Victor Korolev & Andrey Gorshenin & Konstatin Belyaev, 2019. "Statistical Tests for Extreme Precipitation Volumes," Mathematics, MDPI, vol. 7(7), pages 1-20, July.
    6. Victor Korolev & Andrey Gorshenin, 2020. "Probability Models and Statistical Tests for Extreme Precipitation Based on Generalized Negative Binomial Distributions," Mathematics, MDPI, vol. 8(4), pages 1-30, April.
    7. Michael L. Stein, 2021. "A parametric model for distributions with flexible behavior in both tails," Environmetrics, John Wiley & Sons, Ltd., vol. 32(2), March.

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