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Approximations for the Likelihood Ratio Statistic for Hypothesis Testing Between Two Beta Distributions

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Abstract

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.

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Acknowledgements

The authors would like to thank the two Reviewers for their careful reading and constructive comments. This work was partially supported by the Fundação para a Ciência e a Tecnologia (Portuguese Foundation for Science and Technology) through the project UID/MAT/00297/2013 (Centro de Matemática e Aplicações).

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Authors and Affiliations

  1. Centro de Matemática e Aplicações (CMA) and Departamento de Matemática, FCT, UNL, Lisbon, Portugal

    Filipe Marques

  2. Department of Mathematical Sciences, Durham University, Durham, UK

    Frank Coolen & Tahani Coolen-Maturi

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  1. Filipe Marques
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  2. Frank Coolen
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  3. Tahani Coolen-Maturi
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Correspondence to Filipe Marques.

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Marques, F., Coolen, F. & Coolen-Maturi, T. Approximations for the Likelihood Ratio Statistic for Hypothesis Testing Between Two Beta Distributions. J Stat Theory Pract 13, 17 (2019). https://doi.org/10.1007/s42519-018-0021-8

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  • DOI: https://doi.org/10.1007/s42519-018-0021-8

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