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

Abstract

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)

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1980
Accession Number
ADA093000

Entities

People

  • Emanuel Parzen

Organizations

  • Texas A&M University

Tags

DTIC Thesaurus Topics

  • Continuity
  • Convergence
  • Data Analysis
  • Data Mining
  • Data Modeling
  • Data Science
  • Distribution Functions
  • Distribution Theory
  • Information Science
  • New York
  • Order Statistics
  • Probability
  • Probability Distributions
  • Random Variables
  • Statistical Samples
  • Statistics
  • Theorems

Fields of Study

  • Mathematics

Readers

  • Statistical inference.