Shrinkage Methods for Estimating the Shape Parameter of the Generalized Pareto Distribution
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Date
2023
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Journal of Applied Mathematics
Abstract
The generalized Pareto distribution is one of the most important distributions in statistics of extremes as it has wide applications in
fields such as finance, insurance, and hydrology. This study proposes two new methods for estimating the shape parameter of the
generalized Pareto distribution (GPD). The proposed methods use the shrinkage principle to adapt the existing empirical Bayesian
with data-based prior and the likelihood moment method to obtain two estimators. The performance of the proposed estimators is
compared with the existing estimators (i.e., maximum likelihood, likelihood moment estimators, etc.) for the shape parameter of
the generalized Pareto distribution in a simulation study. The results show that the proposed estimators perform better for small to
moderate number of exceedances in estimating shape parameter of the light-tailed distributions and competitive when estimating
heavy-tailed distributions. The proposed estimators are illustrated with practical datasets from climate and insurance studies.
Description
An article published in Journal of Applied Mathematics,Volume 2023, Article ID 9750638, 11 pages
https://doi.org/10.1155/2023/9750638
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Journal of Applied Mathematics Volume 2023, Article ID 9750638, 11 pages, https://doi.org/10.1155/2023/9750638