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Approximations for the likelihood ratio statistic for hypothesis testing between two Beta distributions.

Marques, F.J. and Coolen, F.P.A. and Coolen-Maturi, T. (2019) 'Approximations for the likelihood ratio statistic for hypothesis testing between two Beta distributions.', Journal of statistical theory and practice., 13 . p. 17.


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.

Item Type:Article
Full text:(AM) Accepted Manuscript
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Publisher statement:This is a post-peer-review, pre-copyedit version of an article published in Journal of statistical theory and practice. The final authenticated version is available online at:
Date accepted:13 October 2018
Date deposited:16 October 2018
Date of first online publication:01 November 2018
Date first made open access:01 November 2019

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