Analysis of extreme values of natural processes: statistical description of the maximum

摘要

Analysis of extreme values of time series occupies an important position in the study of many natural and environmental phenomena. This paper describes the statistical descriptors and characteristics of the Type I asymptotic distribution of extreme values for different underlying, or initial, distributions and different values of sample size, or number of observations. Specifically, the parameters (characteristic largest value and intensity function) of the Type I distribution of the maximum value are evaluated for several initial distributions, including the normal, lognormal, and gamma. Two moments (the mean and the variance of the maximum value from sequences of size n from these initial distributions) also are determined, based solely on knowledge of the initial distribution and its descriptors and the sequence, or sample, size. Selected results relevant to other initial distributions also are presented.