Quantile Functions, Convergence in Quantile, and Extreme Value Distribution Theory

摘要

The aim of this paper is to summarize the probability theory of quantile functions. The contributions of this paper are: (1) to emphasize the duality of quantile functions with distribution functions (sec. 1); (2) to explicitly define the notions of 'convergence in quantile' and 'convergence in r-mean quantile' (sec 2); (3) provide simple proofs of the distribution theory of extreme values (sec 4); and (4) emphasize the role of tail exponents of quantile functions and density-quantile functions in providing easy to apply criteria for the extreme value distributions corresponding to a specified distribution. (Author)