An Evaluation of the Efficiency of a Shape Parameter Estimator for the Log-logistic Distribution

The log-logistic distribution has been successfully used in various fields. This model is often presented with shape and scale parameters. This chapter examines recently introduced shape parameter estimators. For additional flexibility, a location parameter can be added resulting in the three-parameter or shifted log-logistic distribution. Different properties of the proposed estimators were obtained and their efficiency was evaluated for finite sample sizes using simulation results. The log-logistic distribution is obtained through the logarithmic transformation of the logistic distribution. This model is widely used in different fields of study. The chapter presents the estimators under study and summarizes their asymptotic properties, including the nondegenerate asymptotic behavior.