Bias-corrected maximum likelihood estimation of the parameters of the generalized half-normal distribution

ABSTRACT

Cooray and Ananda introduced a two-parameter generalized Half-Normal distribution which is useful for modelling lifetime data, while its maximum likelihood estimators (MLEs) are biased in finite samples. This motivates us to construct nearly unbiased estimators for the unknown parameters of the model. In this paper, we adopt two approaches for bias reduction of the MLEs of the parameters of generalized Half-Normal distribution. The first approach is the analytical methodology suggested by Cox and Snell and the second is based on parametric Bootstrap resampling method. Additionally, the method of moments (MMEs) is used for comparison purposes. The numerical evidence shows that the analytic bias-corrected estimators significantly outperform their bootstrapped-based counterpart for small and moderate samples as well as for MLEs and MMEs. Also, it is apparent from the results that bias- corrected estimates of shape parameter perform better than that of scale parameter. Further, the results show that bias-correction scheme yields nearly unbiased estimates. Finally, six fracture toughness real data sets illustrate the application of our methods.

KEYWORDS:

• Bias correction
• generalized Half-Normal distribution
• maximum likelihood estimators
• Monte Carlo simulation

Acknowledgements

The authors would like to thank the Editor-in-Chief, Associate Editor and two referees for careful reading and for comments which greatly improved the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.