Physical Sciences and Mathematics Commons^™

Improved Parameter Estimation Of The Log-Logistic Distribution With Applications, Joseph Reath

Dissertations, Master's Theses and Master's Reports

In this report, we work with parameter estimation of the log-logistic distribution. We first consider one of the most common methods encountered in the literature, the maximum likelihood (ML) method. However, it is widely known that the maximum likelihood estimators (MLEs) are usually biased with a 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, we also consider the generalized moments (GM) …