Numerical maximum log likelihood estimation for generalized lambda distributions

Abstract

This paper presents a two-step procedure using the method of moment or percentile to find initial values and then maximize the numerical log likelihood to fit the appropriate generalized lambda distribution to data. This paper demonstrates the use of this procedure to fit well-known statistical distributions as well as some empirical data. Overall, the use of numerical maximum log likelihood estimation is a valuable alternative among existing methods of fitting. It provides not only convincing results in terms of quantile plots and goodness of fit tests but also has the advantage of a lower variability in its parameter estimation compared to the existing starship ( King and MacGillivray, 1999) and method of moment ( Karian and Dudewicz, 2000) fitting schemes.