A simple and efficient method for finding the closest generalized lambda distribution to a specific model

Abstract The four-parameter Generalized Lambda distribution (GLD) can be used to approximate many probability distributions. We present a simple and efficient two-stage process for finding optimal GLD parameters to approximate a specified distribution. The probability density quantile function is first used to find the best GLD shape parameters. Given those shape parameters, it is then straightforward to find the best location and scale parameters. We highlight the excellent performance of our approach with comparisons to two existing and popular methods for a wide choice of distributions. Finally, we show that this is method can be used with other distributions by providing applications also to the Generalized Beta distribution.