Estimating the Parameters of the Generalized Lambda Distribution (pdf)

Fitting a probability distribution to observed or generated data constitutes an essential part of any data analysis system. The Generalized Lambda Distribution, while extremely versatile in this regard, is also a difficult distribution to fit. Parameter estimation methods that attempt to match moments or quantiles of the data require minimizing a bivariate non-linear function. The suitability of the resulting fitted distribution must be evaluated using a goodness-of-fit test and, if found unacceptable, the minimization procedure must be manually restarted from a new initial point. We propose a parameter estimation method that automatically generates initial points, as necessary, using quasi-random Sobol sequences.