Bias-Corrected maximum likelihood estimation of the parameters of the weighted Lindley distribution

ABSTRACT

The two-parameter weighted Lindley distribution is useful for modeling survival data, whereas its maximum likelihood estimators (MLEs) are biased in finite samples. This motivates us to construct nearly unbiased estimators for the unknown parameters. We adopt a “corrective” approach to derive modified MLEs that are bias-free to second order. We also consider an alternative bias-correction mechanism based on Efron’s bootstrap resampling. Monte Carlo simulations are conducted to compare the performance between the proposed and two previous methods in the literature. The numerical evidence shows that the bias-corrected estimators are extremely accurate even for very small sample sizes and are superior than the previous estimators in terms of biases and root mean squared errors. Finally, applications to two real datasets are presented for illustrative purposes.

KEYWORDS:

• Bias reduction
• Bootstrap
• Maximum likelihood estimators
• Survival data
• Weighted Lindley distribution

MATHEMATICS SUBJECT CLASSIFICATION:

• 62F10
• 62F40
• 62N02
• 62N05

Acknowledgments

The authors thank the editor, the associate editor, and two referees for their constructive and valuable suggestions that have improved the original version of the article. This work was partially supported by the New Faculty Start-Up Fund at Michigan Technological University.