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

Marques, F.J.; Coolen, F.P.A.; Coolen-Maturi, T.

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.

Citation

Marques, F., Coolen, F., & Coolen-Maturi, T. (2019). Approximations for the likelihood ratio statistic for hypothesis testing between two Beta distributions. Journal of statistical theory and practice, 13, Article 17. https://doi.org/10.1007/s42519-018-0021-8

• Journal Article Type: Article
• Acceptance Date: Oct 13, 2018
• Online Publication Date: Nov 1, 2018
• Publication Date: Mar 31, 2019
• Deposit Date: Oct 15, 2018
• Publicly Available Date: Nov 1, 2019
• Journal: Journal of Statistical Theory and Practice
• Electronic ISSN: 1559-8616
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Volume: 13
• Article Number: 17
• DOI: https://doi.org/10.1007/s42519-018-0021-8
• Public URL: https://durham-repository.worktribe.com/output/1316440