科研成果详情

Most statistical approaches assume that all of the data points come from the same distribution. However, in real-life applications the data points come from more than one distribution with no information to identify which observation goes with which distribution. In such cases, the classical extreme value theory can not help us. In this paper, we investigate the extreme value theory of data from more than one distribution based on generalized order statistics under continuous strictly monotone normalization. This paper investigates the asymptotic behaviors of upper and lower extremes generalized order statistics based on a random sample drawn from a finite mixture of distributions normalized by the same continuous strictly monotonic sequence or a mixture of continuous strictly monotonic sequences. For illustration of the usage of our theoretical results, these asymptotic behaviors under linear and power normalization are studied with examples.