A Trivariate Extreme Value Distribution Applied to Flood Frequency Analysis

Area of Science:

• Statistics
• Extreme Value Theory
• Environmental Science

Background:

• Multivariate extreme value distributions are crucial for analyzing joint extreme events.
• Existing models may not adequately capture complex dependencies in high-dimensional data.
• Accurate modeling is essential for risk assessment in environmental and hydrological studies.

Purpose of the Study:

• To derive and describe a novel trivariate extreme value distribution based on the logistic model.
• To develop a generalized maximum likelihood estimation procedure for parameter estimation with varying record lengths.
• To assess the reliability of the estimated parameters and compare the proposed model with existing methods.

Main Methods:

• Derivation of a trivariate extreme value distribution from a multivariate logistic model.
• Construction of the probability distribution and density functions for the proposed model.
• Application of a generalized maximum likelihood estimation for parameter estimation.
• Utilizing relative information ratios to assess parameter reliability.
• Case study in Northern Mexico with six gauging stations.

Main Results:

• The proposed trivariate extreme value distribution was successfully constructed and its functions derived.
• The generalized maximum likelihood estimation procedure effectively handled samples with different record lengths.
• Parameter reliability was assessed using relative information ratios.
• The trivariate model demonstrated competitive or superior performance compared to general extreme value (GEV) distributions in the case study.

Conclusions:

• The derived trivariate extreme value distribution offers a robust framework for analyzing multivariate extremes.
• The generalized maximum likelihood estimation provides a flexible approach for parameter estimation.
• The model shows promise for applications in environmental risk assessment, particularly in regions with limited or varied data.