Distributions of Extreme Values of Sequences of Autocorrelated Random Variables: Final Technical Report

摘要

Research on the probabilistic/statistical analyses of extreme values of environmental phenomena such as air pollutant concentrations, water quality, and natural hazards is summarized. Statistical descriptors and characteristics of the maximum value of independent random variables are discussed, and parameters of the extreme value distributions are evaluated for several initial distributions. Extreme values of sequences of autocorrelated random variables are also examined, and statistical descriptors such as the distribution function of the maximum (and its moments) of dependent sequences are derived analytically. The use of computer experiments to analyze extreme phenomena is explored, with a focus on their use in quantifying the effect of dependence in the underlying sequence on the statistical/mathematical properties of the extreme values.