Approximating Distributions by Extended Generalized Lambda Distribution (XGLD)

The family of four-parameter generalized lambda distributions (GLD) is known for its high flexibility. It provides an approximation of most of the usual statistical distributions (e. g., normal, uniform, lognormal, Weibull, etc.). Although GLD is used in many fields where precise data modeling is required, there are some statistical distributions that could not be estimated with high precision. The main objective of this article is to present an extension of generalized lambda distributions (XGLD) model for estimating statistical distributions. This new method has a considerable precision and high flexibility to fit more probability distribution functions with higher accuracy. Using the existing methods for calculation of GLD parameters, it provides methodology of calculating XGLD parameter measurement algorithmically. The XGLD estimations are computed for some well-known distributions and precision of estimations is compared with that of GLD.