Accession Number : AD0014483
Title : On Distribution - Free Statistics
Descriptive Note : Technical rept.
Corporate Author : WASHINGTON UNIV SEATTLE LAB OF STATISTICAL RESEARCH
Personal Author(s) : Birabaum, Z W ; Rubin, H
Report Date : 24 Jul 1953
Pagination or Media Count : 11
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*.
Descriptors : *PROBABILITY DISTRIBUTION FUNCTIONS , STATISTICS , PROBABILITY , DISTRIBUTION
Subject Categories : Statistics and Probability
Distribution Statement : APPROVED FOR PUBLIC RELEASE