Improved maximum likelihood estimators for the parameters of the Johnson S_B distribution

Abstract

In this article, considering the two-parameter Johnson $S_B$ distribution, bounded on the unit interval, we derived, for the first time, the analytical expressions for bias-reduction of maximum likelihood estimators applying the Cox and Snell methodology. Although, in general, the analytical expressions are difficult to obtain, for the Johnson distribution they were simple and easy to implement. From Monte Carlo simulations, we estimated and compared the regular biases, the Cox and Snell biases and parametric Bootstrap-based biases. Our numerical results revealed that the biases should not be neglected and the bias reduction approaches based on the analytical expressions and Bootstrap are quite and equally efficient. Finally, a real application is presented and discussed.

Keywords:

• Bootstrap bias-correction
• Cox–Snell bias-correction
• Johnson S_B distribution
• maximum likelihood estimators
• Monte Carlo simulation

Acknowledgments

The authors thank the Editor, the Associate Editor, and the referee for careful reading and comments which greatly improved the article.