Comparison of different estimation methods for extreme value distribution

Area of Science:

• Statistics
• Probability Theory
• Extreme Value Theory

Background:

• Extreme value distribution models extreme events.
• Accurate parameter estimation is crucial for reliable predictions.
• Various classical and Bayesian methods exist for parameter estimation.

Purpose of the Study:

• To determine the best estimators for unknown parameters of the extreme value distribution.
• To compare the performance of classical and Bayesian estimation techniques.
• To apply these methods to real-world hydrological data.

Main Methods:

• Employed maximum likelihood, moment, least squares, and L-moments estimators.
• Utilized Bayesian methods including Lindley's approximation and Markov Chain Monte Carlo (MCMC).
• Performed simulation studies to assess bias and mean square error.

Main Results:

• Identified superior classical and Bayesian estimators based on simulation performance.
• Provided asymptotic confidence and Bayesian credible intervals.
• Demonstrated practical application using river flood discharge data.

Conclusions:

• The study offers a comprehensive comparison of extreme value distribution estimators.
• Findings aid in selecting optimal methods for modeling extreme hydrological events.
• The research contributes to robust statistical modeling of rare events.