Estimating the Five Parameter Lambda Distribution Using Moment Based Methods

Abstract

With a flexible probability density
function (p.d.f) and five parameters at its disposal, the five parameter
lambda distribution (FPLD) is suitable for distributional modelling.
However, little research has been carried out on this distribution
to date. And although the most recent published work focuses on how
to apply newly developed estimation techniques, the literature does
not address how to accomplish parametric estimation using existing
well-established estimation methods. Hence, this research shows how
to estimate the FPLD using the methods of moments, probability weighted
moments (PWMs) and linear moments (L-moments) with the specific goal
of determining whether any one method is superior to the others. To
illustrate the proposed methods, the FPLD was fitted to the Standard
Normal distribution. The results show that Standard Normal distribution
was easily approximated by the FPLD using all three estimation techniques.
Overall, the methods of PWM and L-moments were deemed to be superior
to the method of moments despite the fact that neither outperformed
the other according to the goodness of fit tests.