Part 1 The IID case - functional laws of small numbers: functional laws of small numbers - bounds for the functional laws of small numbers, applications; extreme value theory - Von Mises conditions, the peaks over threshold method, initial estimation of the class index; estimation of conditional curves - Poisson process approach, the nonparametric case, the semiparametric case, extension to several points, a nearest neighbour alternative, optimal accuracy of estimators; multivariate maxima - limiting distributions, representations and dependence functions, Max-Stable stochastic processes; multivariate extremes - strong approximation of exceedances, further concepts of extremes, extreme value analysis with XTREMES - artificial data, real grouped data, real continuous data. Part 2 Non IID observations: introduction to the non IID case - definitions, stationary random sequences, independent random sequences, nonstationary random sequences; extremes of random sequences - introduction and general theory, stationary sequences, independent sequences, nonstationary sequences; extremes of Gaussian processes - stationary Gaussian processes, nonstationary Gaussian processes, empirial characteristic functions; extensions for rare events - rare events of random sequences, the point process of exceedances, application to peaks over threshold, application to rare events, triangular arrays of rare events, multivariate extremes of non IID sequences; statistics of extremes - application to ecological data, frost data; appendix - user's guide to XTREMES - getting started, preparations, becoming acquainted with XTREMES, hot keys, window options and help menus; XTREMES in action - implemented distributions, generating and reading data, nonparametric estimation, estimation in the alpha-mode, estimation in the beta-mode, simulations, important facilities and advice.
