Approximations for the likelihood ratio statistic for hypothesis testing between two beta distributions

Filipe Marques, Frank Coolen, Tahani Coolen-Maturi

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


In this paper, the likelihood ratio to test between two Beta distributions is addressed. The exact distribution of the likelihood ratio statistic, for simple hypotheses, is obtained in terms of Gamma or Generalized Integer Gamma distributions, when the first or the second of the two parameters of the Beta distributions are equal and integers. In the remaining cases addressed, near-exact or asymptotic approximations are developed for the likelihood ratio statistic. Both the exact, asymptotic or near-exact representations are obtained using a logarithm transformation of the likelihood ratio statistic and by working with the corresponding characteristic function. The numerical studies illustrate the precision of the approximations developed. Simulations are developed to analyse the power and the reproducibility probability of the tests.

Original languageEnglish
Article number17
JournalJournal of Statistical Theory and Practice
Issue number1
Publication statusPublished - Mar 2019


  • Generalized Integer Gamma distribution
  • Generalized Near-Integer Gamma distribution
  • Likelihood ratio tests
  • Mixtures
  • Nonparametric predictive inference
  • Reproducibility probability


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