TY - JOUR

T1 - Approximations for the likelihood ratio statistic for hypothesis testing between two beta distributions

AU - Marques, Filipe

AU - Coolen, Frank

AU - Coolen-Maturi, Tahani

N1 - This work was partially supported by the Fundacao para a Ciencia e a Tecnologia (Portuguese Foundation for Science and Technology) through the project UID/MAT/00297/2013 (Centro de Matematica e Aplicacoes).

PY - 2019/3

Y1 - 2019/3

N2 - 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.

AB - 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.

KW - Generalized Integer Gamma distribution

KW - Generalized Near-Integer Gamma distribution

KW - Likelihood ratio tests

KW - Mixtures

KW - Nonparametric predictive inference

KW - Reproducibility probability

UR - http://www.scopus.com/inward/record.url?scp=85082191931&partnerID=8YFLogxK

U2 - 10.1007/s42519-018-0021-8

DO - 10.1007/s42519-018-0021-8

M3 - Article

AN - SCOPUS:85082191931

VL - 13

JO - Journal of Statistical Theory and Practice

JF - Journal of Statistical Theory and Practice

SN - 1559-8608

IS - 1

M1 - 17

ER -