Improved parameter estimation of the log-logistic distribution with applications

In this paper, we deal with parameter estimation of the log-logistic distribution. It is widely known that the maximum likelihood estimators (MLEs) are usually biased in the case of the finite sample size. This motivates a study of obtaining unbiased or nearly unbiased estimators for this distribution. Specifically, we consider a certain ‘corrective’ approach and Efron’s bootstrap resampling method, which both can reduce the biases of the MLEs to the second order of magnitude. As a comparison, the commonly used generalized moments method is also considered for estimating parameters. Monte Carlo simulation studies are conducted to compare the performances of the various estimators under consideration. Finally, two real-data examples are analyzed to illustrate the potential usefulness of the proposed estimators, especially when the sample size is small or moderate.