Computer experiments for the analysis of extreme-value phenomena

摘要

The analysis of extreme values occupies an important role in the study of many physical phenomena. In many instances, measurements of the phenomenon of interest form a time series in which successive observations are statistically dependent (i.e., autocorrelated), and frequently the probabilities of occurence of extreme values of such sequences are of interest. However, the presence of autocorrelation very often does not permit analytical approaches for obtaining such probabilities and related statistical properties. This study proposes the use of computer experiments in the analysis of extreme-value phenomena in such cases, and, in particular, the use of computer experiments to quantify the effect of dependence in the underlying sequence on the statistical properties of the extreme values. Computer experiments are described for the investigation of the statistical behavior of the maximum value of an underlying sequence exhibiting an exponential-type correlation structure. Statistical descriptors of the maximum such as its distribution functions and selected moments (e.g., mean and variance) are determined, and the effects of varying degrees of autocorrelation are quantified. Effects of other variables, such as the size of the underlying sequences, also are examined and discussed.