New results on the likelihood ratio and score tests for the von Mises distribution

Abstract

In this paper, we derive Bartlett and Bartlett-type corrections [G.M. Cordeiro and S.L.P. Ferrari 1991, A modified score test statistic having chi-squared distribution to order n ⁻¹ , Biometrika 78 (1991), pp. 573–582] to improve the likelihood ratio and Rao's score statistics for testing the mean parameter and the concentration parameter in the von Mises distribution. Simple formulae are suggested for the corrections valid for small and large values of the concentration parameter that do not depend on the modified Bessel functions and can be useful in practical applications.

Keywords:

• Bartlett corrections
• Bartlett-type corrections
• likelihood ratio
• score statistic

Acknowledgements

The authors acknowledge financial support from CNPq, Brazil. They are also grateful to an anonymous referee for helpful comments and suggestions that improved this paper.