Date of Award
2016
Document Type
Open Access Master's Report
Degree Name
Master of Science in Mathematical Sciences (MS)
Administrative Home Department
Department of Mathematical Sciences
Advisor 1
Min Wang
Committee Member 1
Renfang Jiang
Committee Member 2
Yu Cai
Abstract
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) method. 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.
Recommended Citation
Reath, Joseph, "IMPROVED PARAMETER ESTIMATION OF THE LOG-LOGISTIC DISTRIBUTION WITH APPLICATIONS", Open Access Master's Report, Michigan Technological University, 2016.