Using Simple Fixed-Point Iterations to Estimate Generalized Pareto Distribution Parameters

Estimating generalised Pareto distribution (GPD) parameters is a fundamental step in modelling the extremevalue distribution of random variables. It is generally done with the maximum likelihood method, but there are generally difficulties in estimating GPD parameters using this method as there is n...

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Bibliographic Details
Published in:IAENG international journal of applied mathematics 2024-02, Vol.54 (2), p.194-204
Main Authors: Purwani, Sri, Ibrahim, Riza Andrian
Format: Article
Language:English
Subjects:
Earthquakes
Extreme values
Iterative methods
Mathematical models
Maximum likelihood method
Modelling
Numerical analysis
Numerical methods
Parameter estimation
Random variables
Simulation
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Summary:Estimating generalised Pareto distribution (GPD) parameters is a fundamental step in modelling the extremevalue distribution of random variables. It is generally done with the maximum likelihood method, but there are generally difficulties in estimating GPD parameters using this method as there is no closed-form solution for the first derivative of the GPD log-likelihood function. This makes the solution difficult to determine analytically. However, numerical methods can be used as an alternative. Therefore, this study estimates the solution numerically using a simple fixed-point iteration method that is intuitive for both practitioners and professionals. We obtained three fixed-point iterations when estimating GPD parameters that met the unbiased estimator and convergence criteria. The iterations allow practitioners and professionals to directly and efficiently estimate GPD parameters when modelling extreme-value distributions of random variables.
ISSN:1992-9978
1992-9986