M-estimation of log-logistic distribution parameters with outliers

Abstract

Log-logistic distribution is widely-used in the analysis of agricultural, survival, hydrological and economics data. Therefore, its parameters have to be estimated accurately. Generally, traditional estimators such as maximum likelihood, moment and least squares are used to estimate the parameters of log-logistic distribution. However, it is known that these estimators are very sensitive to outliers and thus, they can cause inconsistent results. In this study, we consider M-estimators, one of alternative robust regression methods, to estimate the parameters of the log-logistic distribution for both data with outliers and without outliers. The simulation results show that most of the considered M-estimators for shape parameter out perform traditional estimators in terms of mean squared error for small sample sizes or data with outliers. Moreover, two real life applications are provided to show the feasibility of M-estimators.