Extremes of Correlated Non‐Gaussian Series

Abstract

Mean crossings rates are determined for translation series, which can be obtained from correlated Gaussian series by nonlinear transformations. Translation series have a specified marginal distribution and correlation structure. It is shown that mean crossing rates depend weakly on correlation, particularly for relatively large thresholds. This weak dependence shows that approximations can be developed for mean crossing rates if correlation is disregarded. Theoretical developments are applied to determine the reliability of chain systems with links having correlated, non‐Gaussian resistances and to estimate extreme wind speeds.