Test for homogeneity in gamma mixture models using likelihood ratio

Tony Siu Tung WONG, Wai Keung LI

Research output: Contribution to journalArticlespeer-review

9 Citations (Scopus)


A testing problem of homogeneity in gamma mixture models is studied. It is found that there is a proportion of the penalized likelihood ratio test statistic that degenerates to zero. The limiting distribution of this statistic is found to be the chi-bar-square distributions. The degeneration is due to the negative-definiteness of a complicated random matrix, depending on the shape parameter under the null hypothesis. In light of this dependency, bounds on the distribution are introduced and a weighted average procedure is proposed. Simulation suggests that the results are accurate and consistent, and that the asymptotic result applies to the maximum likelihood estimator, obtained via an Expectation–Maximization algorithm. Copyright © 2013 Elsevier B.V. All rights reserved.
Original languageEnglish
Pages (from-to)127-137
JournalComputational Statistics and Data Analysis
Early online dateSept 2013
Publication statusPublished - Feb 2014


Wong, T. S. T., & Li, W. K. (2014). Test for homogeneity in gamma mixture models using likelihood ratio. Computational Statistics and Data Analysis, 70, 127-137. doi: 10.1016/j.csda.2013.09.001


  • Chi-bar-square distributions
  • Gamma mixture
  • Likelihood ratio
  • Maximum likelihood
  • Negative-definite


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