Distribution of the LR criterion Up,m,n as a marginal distribution of a generalized Dirichlet model
The density of the likelihood ratio criterion Up,m,n is expressed in terms of a marginal density of a generalized Dirichlet model having a specific set of parameters. The exact distribution of the likelihood ratio criterion so obtained has a very simple and general format for every p . It provides an easy and direct method of computation of the exact p -value of Up,m,n . Various types of properties and relations involving hypergeometric series are also established.
T.W. ANDERSON, (2003), An Introduction to Multivariate Statistical Analysis, John Wiley & Sons, New Jersey.
M. BILODEAU, D. BRENNER, (1999), Theory of Multivariate Statistics, Springer-Verlag, New York.
C.A. COELHO, (1998), The generalized integer gamma distribution-A basis for distributions in multivariate statistics, “Journal of Multivariate Analysis”, 64, pp. 86-102.
R.J. CONNOR, J.E. MOSIMANN, (1969), Concepts of independence for proportions with a generalization of the Dirichlet distribution, “Journal of American Statistical Association.”, 64, pp. 194-206.
R.H.A. LOCHNER, (1975), A generalized Dirichlet distribution in Bayesian life testing, “Journal of the Royal Statistical Society”, series B, 37, pp. 103-113.
A.M. MATHAI, (1971), On the distribution of the likelihood ratio criterion for testing linear hypotheses on regression coefficients, “The Annals of Institute of Statistical Mathematics”, 23, pp. 181-197.
A.M. MATHAI, (1993), A Handbook of Generalized Special Functions for Statistical and Physical Sciences, Oxford University Press, Oxford.
K.C.S. PILLAI, A.K. GUPTA, (1969), On the exact distribution of Wilks' criterion, “Biometrika”, 56, pp. 109-118.
A.C. RENCHER, (1998), Multivariate Statistical Inference and Applications, John Wiley & Sons, New York.
M. SCHATZOFF, (1966), Exact distributions of Wilks' likelihood ratio criterion, “Biometrika”, 53, pp. 347-358.
S. THOMAS, S. GEORGE, (2004), A review of Dirichlet distribution and its generalizations, “Journal of the Indian Society for Probability and Statistics”, 8, pp. 72-91.
S. THOMAS, A. THANNIPPARA, (2008), Distribution of the Λ -criterion for sphericity test and its connection to a generalized Dirichlet model, “Communicatoins in Statistics - Simulation and Computation”, 37, pp. 1385-1395.