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

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.