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One‐Way Classification ANOVA Model for the Mixture of Two Multivariate Normal Populations
Author(s) -
Gupta A. K.,
Kabe D. G.
Publication year - 1991
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710330320
Subject(s) - wishart distribution , mathematics , multivariate statistics , statistics , rank (graph theory) , matrix t distribution , multivariate analysis of variance , multivariate normal distribution , covariance , inverse wishart distribution , covariance matrix , matrix normal distribution , multivariate analysis , statistical hypothesis testing , combinatorics
When a sample of size n is available from a mixture of two normal populations with different mean vectors and a common covariance matrix, S RIVASTAVA and A WAN (1982) develop one‐way A NOVA analysis for testing a certain composite linear hypothesis. They show that the error and hypothesis sum of products matrices have independent noncentral Wishart densities of rank unity each. However, they do not obtain the necessary Wilks' λ for testing the desired hypothesis. The present paper obtains the density of λ. This density is doubly noncentral multivariate beta density. The derivation is based on generalized Sverdrup's lemmas, K ABE (1965), (1974).