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Approximating the Non‐Null Distribution of the Likelihood Ratio Test Statistic
Author(s) -
Lawal H. B.
Publication year - 1992
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.4710340408
Subject(s) - mathematics , likelihood ratio test , statistics , null distribution , test statistic , statistic
This paper is concerned with investigation into the behavior of the likelihood ratio test statistic G 2 when the alternative hypothesis M (Q Q ) is the true model. Exact moments of G 2 are computed empirically and three approximations are considered for approximating the non‐null distribution of G 2 . Our results show that the two parameter gamma distribution provides a closer approximation to the exact powers of G 2 . A randomized procedure was employed to obtain critical values based on 1000 simulated samples.