Quantile Functions, Convergence in Quantile, and Extreme Value Distribution Theory.
TEXAS A AND M UNIV COLLEGE STATION INST OF STATISTICS
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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
- Statistics and Probability