Janet E. Heffernan

Dependence Measures for Extreme Value Analyses

Quantifying dependence is a central theme in probabilistic and statistical methods for multivariate extreme values. Two situations are possible: one where, in a limiting sense, the extremes are dependent; the other where, in the same sense, the extremes are independent. This paper comprises an overview of the principal issues through a unified approach which encompasses both these situations. Novel diagnostic measures for dependence are also developed which provide complementary information about different aspects of extremal dependence. The paper is written in an elementary style, with the methodology illustrated by application to theoretical examples and typical data-sets. These data-sets and the S-plus functions used for the analyses are available online.

A Directory of Coefficients of Tail Dependence

Models characterizing the asymptotic dependence structures of bivariate distributions have been introduced by Ledford and Tawn (1996), among others, and diagnostics for such dependence behavior are presented in Coles et al. (1999). The following pages are intended as a supplement to the papers of Ledford and Tawn and Coles et al. In particular we focus on the coefficient of tail dependence, which we evaluate for a wide range of bivariate distributions. We find that for many commonly employed bivariate distributions there is little flexibility in the range of limiting dependence structure accommodated. Many distributions studied have coefficients of tail dependence corresponding to near independence or a strong form of dependence known as asymptotic dependence.

Extreme Value Analysis of a Large Designed Experiment: A Case Study in Bulk Carrier Safety

The bulk carrier M.V. Derbyshire sank in 1980 when she encountered a typhoon near Japan. The most likely cause of her loss was finally explained in the report of the Re-opened Formal Investigation in 2000. The report also revealed inadequacies in safety standards for such vessels, particularly concerning regulations governing hatch cover strengths, and requested further work be undertaken to examine the sufficiency of aspects of the existing international standards for ship design. This paper describes the extreme value analysis of data from a large designed experiment intended to aid the revision of these safety standards. We highlight the importance of consistency of results over the different conditions examined, and how this can be achieved using various data pooling and regression techniques.

An extreme value analysis for the investigation into the sinking of the M. V. Derbyshire

The paper describes our involvement in the high court reopened formal investigation into the sinking of the bulk carrier M. V. Derbyshire. The statistical problem that we addressed concerned the estimation of the probability that the ship had sunk from a particular form of structural failure, resulting from large wave impacts on the ship, for each of a range of possible sea-state and vessel conditions. We considered several statistical models for the wave impacts on the ship with the generalized Pareto distribution, motivated by extreme value theory, providing an excellent description and aiding the investigation to draw clear conclusions about the cause of the sinking. Copyright 2003 Royal Statistical Society.