A Note on Bias Correction for the Standard Two-Sided Power Distribution

It is verified that the maximum likelihood (ML) estimators of the standard two-sided power distribution (STSP) parameters introduced by van Dorp and Kotz on the interval (0,1) can be severely biased. Since the usual analytical methods of bias correction cannot be applied in such a parametric distribution, bootstrap bias correction methods are proposed. The numerical study favors a particular bootstrap estimator based on parametric resampling. Real data applications are also considered to illustrate the impact of bias correction of the usual maximum likelihood estimators of the standard two-sided power distribution parameters when the sample size is small. Bias-corrected bootstrap estimators for the standard two-sided power distribution are developed. The bias-corrected bootstrap estimators produce substantial bias reduction relative to the maximum likelihood estimators, with the parametric bias-corrected bootstrap estimators being better than the nonparametric bias-corrected bootstrap estimators.image

Automated summary

It is confirmed that the maximum likelihood estimators of the standard two-sided power distribution parameters introduced by van Dorp and Kotz can be biased. To address this issue in a parametric distribution, bootstrap bias correction methods are proposed. The study shows that the parametric bootstrap estimator, based on resampling, is favored. Real data applications further illustrate the effectiveness of bias correction for small sample sizes.