Bias Correction in the Type I Generalized Logistic Distribution

Abstract

Four strategies for bias correction of the maximum likelihood estimator of the parameters in the Type I generalized logistic distribution are studied. First, we consider an analytic bias-corrected estimator, which is obtained by deriving an analytic expression for the bias to order n ⁻¹; second, a method based on modifying the likelihood equations; third, we consider the jackknife bias-corrected estimator; and fourth, we consider two bootstrap bias-corrected estimators. All bias correction estimators are compared by simulation. Finally, an example with a real data set is also presented.

Keywords:

• Bias correction
• Bootstrap
• Jackknife
• Maximum likelihood estimator
• Type I generalized logistic distribution

Mathematics Subject Classification:

• 62F10
• 62F40

Acknowledgments

The authors thank the anonymous referees for their constructive comments and suggestions which helped to improve the presentation. The research in this article has been partially supported by grant DIUC 210.014.018-1.0 (Universidad de Concepción, Chile) and MTM2008-00018 (Ministerio de Ciencia e Innovación, Spain).