Estimating the Five Parameter Lambda Distribution Using Moment Based Methods

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.