On Distribution - Free Statistics

Abstract

The concepts of distribution-free statistics and statistics of structure (d) were defined relative to families Omega and Omega' of cumulative probability functions. A counter example was presented to disprove the conjecture that every distribution-free statistic, symmetric in X1, X2...., Xn (a sample of a 1-dimensional random variable X with a continuous cumulative probability function F) with Omega = Omega' = Omega 2, has structure (d). Strongly distribution-free statistics in a family Omega* with respect to Omega' were defined, and a proof was presented of the equivalence of statistics of structure (d) and strongly distribution-free statistics under the condition that Omega = Omega' = Omega*.

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Document Details

Document Type
Technical Report
Publication Date
Jul 24, 1953
Accession Number
AD0014483

Entities

People

  • H. Rubin
  • Z. W. Birabaum

Organizations

  • University of Washington

Tags

DTIC Thesaurus Topics

  • Distribution Functions
  • Intervals
  • Probability
  • Probability Distributions
  • Random Variables
  • Statistics
  • Universities

Fields of Study

  • Mathematics

Readers

  • Analytical Mechanics
  • Regression Analysis.