Quantile Based Unified Distribution of Extreme Values and Order Statistics.

Abstract

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) or X(t) > Q(u). (Author)

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Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1987
Accession Number
ADA185171

Entities

People

  • Emanuel Parzen

Organizations

  • Texas A&M University

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Asymptotic Normality
  • Data Analysis
  • Data Mining
  • Data Science
  • Distribution Functions
  • Distribution Theory
  • Information Science
  • Normal Distribution
  • Order Statistics
  • Probability
  • Probability Density Functions
  • Probability Distributions
  • Random Variables
  • Statistical Samples
  • Statistics
  • Theorems
  • Universities

Fields of Study

  • Mathematics

Readers

  • Analytical Mechanics
  • Statistical inference.