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 one-sided 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