Characterizing Log-Logistic (LL) Distributions through Methods of Percentiles and L-Moments

Abstract

The main purpose of this paper is to characterize the log-logistic (LL) distributions through the methods of percentiles and L-moments and contrast with the method of (product) moments. The method of (product) moments (MoM) has certain limitations when compared with method of percentiles (MoP) and method of L-moments (MoLM) in the context of fitting empirical and theoretical distributions and estimation of parameters, especially when distributions with greater departure from normality are involved. Systems of equations based on MoP and MoLM are derived. A methodology to simulate univariate LL distributions based on each of the two methods (MoP and MoLM) is developed and contrasted with MoM in terms of fitting distributions and estimation of parameters. Monte Carlo simulation results indicate that the MoPand MoLM-based LL distributions are superior to their MoM based counterparts in the context of fitting distributions and estimation of parameters.