MULTIVARIATE DISTRIBUTIONS OF MAXIMA AND EXTREMES FOR GAUSSIAN VECTOR-PROCESSES

A new class of multivariate extensions of probability distributions related to local maxima and extremes for scalar Gaussian processes are considered. Joint statistics of the radius vector magnitude and the corresponding direction vector constitute the basis for the present approach. The asymptotic behaviour of the distributions is also investigated. The influence from basic process characteristics on the shape of the density functions are studied. Application of the extreme value distributions for evaluation of reliability is disclosed. Numerical results are presented for a specific example. Finally, the relevance of the so-called expected extreme hypersurfaces is illustrated in connection with a given design formulation.