
Accession Number : AD0701361
Title : A BOUND ON THE CLASSIFICATION ERROR FOR DISCRIMINATING BETWEEN POPULATIONS WITH SPECIFIED MEANS AND VARIANCES.
Descriptive Note : Technical rept.,
Corporate Author : STANFORD UNIV CALIF DEPT OF STATISTICS
Personal Author(s) : Chernoff ,Herman
Report Date : 05 JAN 1970
Pagination or Media Count : 15
Abstract : Given two univariate distribution functions F sub 1 and F sub 2 with means and variances mu sub 1, mu sub 2, (sigma sub 1) squared, (sigma sub 2) squared, Becker((1968), Recognition of Patterns, Polyteknisk Forlag, Copenhagen) has proposed S = (absolute value of (mu sub 1 mu sub 2))/(sigma sub 1 + sigma sub 2) as a measure of separability of F sub 1 and F sub 2. He has conjectured that of all pairs F sub 1, F sub 2 with specified means and variances, the worst pair using onesided tests based on a single observation yields an error probability of (2(1 + S squared)) exp (1) when F sub 1 and F sub 2 are equally likely. In this paper the conjecture is verified and a related conjecture is shown to apply equally well to the likelihood ratio test. (Author)
Descriptors : (*STATISTICAL DISTRIBUTIONS, CLASSIFICATION), (*PATTERN RECOGNITION, CLASSIFICATION), STATISTICAL TESTS, DISTRIBUTION FUNCTIONS, SAMPLING, ERRORS, THEOREMS
Subject Categories : Statistics and Probability
Cybernetics
Distribution Statement : APPROVED FOR PUBLIC RELEASE