
Accession Number : AD0656588
Title : NORMIX: COMPUTATIONAL METHODS FOR ESTIMATING THE PARAMETERS OF MULTIVARIATE NORMAL MIXTURES OF DISTRIBUTIONS.
Descriptive Note : Research memo.,
Corporate Author : NAVAL PERSONNEL RESEARCH ACTIVITY SAN DIEGO CALIF
Personal Author(s) : Wolfe,John H.
Report Date : AUG 1967
Pagination or Media Count : 38
Abstract : Procedures are described for estimating the means, covariances, and mixing proportions of a mixture of multivariatenormal distributions. First, it is shown that the maximumlikelihood estimates must satisfy a certain set of simultaneous equations. The coefficients necessary for a complete NewtonRaphson iterative solution of the equations are presented. Since these coefficients are rather complicated, a simpler and more intuitivelyappealing iterative method is presented and partially justified on the basis that the two iterative methods are approximately the same when the component distributions are wellseparated. The formulas for the simplified iteration involve the familiar statistics of sums and sums of squares and crossproducts with the modification that each sample value is weighted by its relative likelihood of membership in the type whose parameters are being estimated. Since the estimation procedure is basically maximumlikelihood, tests of hypotheses on the number of component distributions can be developed using likelihood ratios. The computational feasibility of the iteration methods is demonstrated in an example in which a computer program to perform the iterations was run on an artificiallyconstructed mixture of three bivariate normal distributions. A discussion of potential applications indicates that the method has promise in the fields of personality typology, social class analysis, biological taxonomy, information retrieval and artificial intelligence.
Descriptors : (*DISTRIBUTION THEORY, MULTIVARIATE ANALYSIS), APPROXIMATION(MATHEMATICS), ITERATIONS, SIMULTANEOUS EQUATIONS, SAMPLING, STATISTICAL ANALYSIS, COMPUTER PROGRAMS, PATTERN RECOGNITION
Subject Categories : Statistics and Probability
Distribution Statement : APPROVED FOR PUBLIC RELEASE