Abstract
In this paper, we consider several families of closed-form estimators of the two parameters of the Generalized Pareto Distribution (GPD). These estimators are easy to compute and have high efficiency when compared to previously proposed methods. We also consider some estimators which are not of closed-form. All methods are based on certain order statistics. The proposed procedures are best for extreme values of the shape parameters and sample sizes of 100 or larger. Monte Carlo simulations are conducted to investigate the performance of the proposed parameter estimation procedures. Our findings suggest that the proposed estimation methods are competitive compared to the existing methods. We provide a real data application to illustrate the utilization of the proposed methods in estimating the GPD parameters.
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The authors sincerely thank the Associate Editor and the referee for their comments which resulted in this improved version of the work.
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Handling Editor: Luiz Duczmal.
Appendix
Appendix
The proposed efficient new estimators of the GPD parameters are implemented as an R package called EfficientClosedGPD, freely available on GitHub. For instance, the GPD parameters based on the methods M1, M2, M3, QM, POS, and LCVM can be obtained as follows.
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From, S.G., Ratnasingam, S. Some efficient closed-form estimators of the parameters of the generalized Pareto distribution. Environ Ecol Stat 29, 827–847 (2022). https://doi.org/10.1007/s10651-022-00548-1
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DOI: https://doi.org/10.1007/s10651-022-00548-1