Accession Number : AD0286382

Title :   ON A SELECTION AND RANKING PROCEDURE FOR GAMMA POPULATIONS

Corporate Author : STANFORD UNIV CALIF APPLIED MATHEMATICS AND STATISTICS LABS

Personal Author(s) : GUPTA,SHANTI S.

Report Date : 06 AUG 1962

Pagination or Media Count : 1

Abstract : The problem of selecting a subset of k gamma populations which includes the ''best'' population, i.e. the one with the largest value of the scale parameter, is studied as a multiple decision problem. The shape parameters of the gamma distributions are assumed to be known and equal for all the k po ulations. Based on a common number of observations from each population, a procedure R is defined which selects a subset which is never empty, small in size and yet large enough to guarantee with preassigned probability that it includes the best population regardless of the true unknown values of the scale parameters 0-i. Expression for the probability of a correct selection using R are derived and it is shown that for the case of a com on number of observations the infimum of this probability is identical with the probability integral of the ratio of the maximum of k-1 independent gamma chance variables to another independent gamma chance variable, all with the same value f the other parameter. It is hown that this function attains its maximum when the parameters 0-i are equal. (Author)

Descriptors :   (*ANALYSIS OF VARIANCE), (*STATISTICAL DISTRIBUTION), *GROUPS(MATHEMATICS))

Distribution Statement : APPROVED FOR PUBLIC RELEASE