Parameter Estimation for the Log-Logistic Distribution Based on Order Statistics

Abstract

In this paper, we discuss the moments and product moments of the order statistics in a sample of size n drawn from the log-logistic distribution. We provide more compact forms for the mean, variance and covariance of order statistics. Parameter estimation for the log-logistic distribution based on order statistics is studied. In particular, best linear unbiased estimators (BLUEs) for the location and scale parameters for the log-logistic distribution with known shape parameter are studied. Hill estimator is proposed for estimating the shape parameter.

Keywords

• log-logistic distribution
• moments
• order statistics
• best linear unbiased estimators
• recurrence relations
• Hill estimator