Asymptotic Behavior of Intermediate Order Statistics: The Infinite Endpoint Case.

Abstract

Suppose X1, X2, ... is a sequence of independent and identically distributed random variables with marginal distribution function F(x) = P(X1 < or = x) satisfying F(x) > 0 for all real x. Let X(k sub n) superscript n denote the (k sub n)th smallest order statistic of the sample X1, ..., Xn, where k sub n/n approaches 0 as n approaches infinity. An almost sure representation of X(k sub n) superscript n in terms of the empirical distribution function is established. The conditions imposed upon F include those under which it is known that X(k sub n) superscript n is asymptotically normal. From the representation the law of the iterated logarithm for X(k sub n) superscript n is obtained. Examples illustrating the general result are presented. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1977
Accession Number
ADA052314

Entities

People

  • Vernon Watts

Organizations

  • Florida State University

Tags

DTIC Thesaurus Topics

  • Asymptotic Normality
  • Data Science
  • Distribution Functions
  • Information Science
  • Military Research
  • Normality
  • Numbers
  • Order Statistics
  • Probability
  • Random Variables
  • Real Numbers
  • Sequences
  • Statistics

Fields of Study

  • Mathematics

Readers

  • Analytical Mechanics
  • Approximation Theory.
  • Regression Analysis.