A survey on computing Lévy stable distributions and a new MATLAB toolbox

Lévy stable distributions have been playing an increasing role in many diverse scientific and engineering fields. However, it is well known that its analytical expression is largely not available, and thus numerical solution becomes essential in the use of Lévy statistics. This article makes a survey on various numerical approaches available today to calculate statistical quantities of Lévy stable distributions. And then based on this investigation, we introduce a new MATLAB toolbox, called LSD, to evaluate statistical quantities of Lévy stable distributions, such as density and distribution functions, random numbers, parameters estimate, and goodness of data fitting. The LSD, first developed using GUI of MATLAB, is very easy to use with a friendly graphical user interface and can provide extremely precise calculations of high significant figures. As a powerful toolbox for signal processing, the LSD is also an open source software package and meets the high demand of easy, accurate and precise evaluation of various quantities of Lévy stable distributions.

► We make a comprehensive survey on numerical methods for Lévy stable distributions. ► The methods of choice are pointed out based on computational accuracy and efficiency. ► We develop a new open-source MATLAB toolbox for Lévy stable distributions, called LSD. ► The LSD has a friendly graphical user interface, first developed using GUI of MATLAB. ► The LSD can evaluate various quantities of Lévy stable distributions efficiently.