Gaussian quadrature method for GLD parameter estimation

Abstract

Generalized lambda distribution (GLD) is a very flexible distribution that has many applications in estimating the distribution of real data. Its flexibility is due to its λs parameters that each of them somehow determine the form of distribution. Since the shape of distribution is very sensitive to the changes of each λs , the smallest error in estimating each parameter results in an error in other parameters, and then resulting in a total error in estimating the data distribution. One of the most accurate and widely used methods for estimating GLD parameters is the momentum method, which requires integral calculations. This paper uses Gaussian quadrature to integrate GLD equations. The results show that in terms of both percentile index and momentum comparison, the new method leads to more accurate calculation of the GLD parameters.