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.