Distribution of the LR criterion Up,m,n as a marginal distribution of a generalized Dirichlet model
DOI:
https://doi.org/10.6092/issn.1973-2201/3541Abstract
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.
References
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.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2008 Statistica
Copyrights and publishing rights of all the texts on this journal belong to the respective authors without restrictions.
This journal is licensed under a Creative Commons Attribution 4.0 International License (full legal code).
See also our Open Access Policy.
