Models for exceedances over high thresholds. (English) Zbl 0706.62039

Davison, A. C.; Smith, R. L.

J. R. Stat. Soc., Ser. B 52, No. 3, 393-442 (1990).

Summary: We discuss the analysis of the extremes of data by modelling the sizes and occurrence of exceedances over high thresholds. The natural distribution for such exceedances, the generalized Pareto distribution, is described and its properties elucidated. Estimation and model-checking procedures for univariate and regression data are developed, and the influence of and information contained in the most extreme observations in a sample are studied. Models for seasonality and serial dependence in the point process of exceedances are described. Sets of data on river flows and wave heights are discussed, and an application to the siting of nuclear installations is described.

MSC:

62F99	Parametric inference
62M10	Time series, auto-correlation, regression, etc. in statistics (GARCH)

Keywords:

generalized extreme value distribution; maximum likelihood; peaks over threshold; profile likelihood; return level; exceedances over high thresholds; generalized Pareto distribution; model-checking procedures; regression; seasonality; serial dependence; point process of exceedances; data on river flows; wave heights; siting of nuclear installations

Software:

GLIM