Quantile Based Unified Distribution of Extreme Values and Order Statistics

摘要

This paper presents ideas leading to unified formulas for exact and asympotic distributions of central and extreme order statistics of random samples and stationary time series X(t) in terms of quantile functions Q(u), density quantile functions fQ(u), left and right hazard quantile functions hQ(u), defined to equal respectively fQ(u)/u and fQ(u)/(1-u), tail exponents, and the spectral density near zero frequency of a two-valued time series c(x(t);u), equal to 1-u or -u as X(t) Q(u). (Author)