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Baseline Methods for the Parameter Estimation of the Generalized Pareto Distribution.

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Baseline Methods for Bayesian Inference in Gumbel Distribution.

Jacinto Martín1, María Isabel Parra1, Mario Martínez Pizarro2

  • 1Departamento de Matemáticas, Facultad de Ciencias, Universidad de Extremadura, 06006 Badajoz, Spain.

Entropy (Basel, Switzerland)
|December 8, 2020
PubMed
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New Bayesian methods improve extreme value analysis by utilizing all data, unlike traditional approaches that discard information. These methods enhance parameter estimation for extreme value distributions, offering more robust insights.

Keywords:
Bayesian inferenceGumbel distributionhighly informative priorsmall dataset

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Area of Science:

  • Statistics
  • Extreme Value Theory
  • Bayesian Inference

Background:

  • Traditional extreme value estimation methods often discard significant amounts of data, particularly when using block maxima.
  • This data wastage leads to suboptimal parameter estimation and reduced statistical power in extreme value analysis.

Purpose of the Study:

  • To develop novel Bayesian methods for extreme value distribution parameter estimation that utilize the entire dataset.
  • To improve upon existing methods by leveraging the relationship between baseline and block maxima distributions.

Main Methods:

  • Proposed two Bayesian estimation methods: Baseline Distribution Method (BDM) and Improved Baseline Method (IBDM).
  • BDM estimates baseline parameters using all data, then transforms to block maxima parameters.
  • IBDM refines BDM by using its output to create an improved prior, prioritizing block maxima data.

Main Results:

  • Empirical comparison with standard Bayesian analysis using non-informative priors was conducted.
  • Simulations involved three baseline distributions (Gumbel, Exponential, Normal) leading to Gumbel extreme distributions.
  • The proposed methods demonstrated potential for more efficient use of available data.

Conclusions:

  • The developed Bayesian methods offer a more comprehensive approach to extreme value parameter estimation.
  • IBDM provides a refinement by allowing greater emphasis on block maxima data.
  • These methods present a valuable alternative for analyzing extreme events when complete data utilization is desired.