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

Authors:
Yingjie Liang;Wen Chen
Affiliations:
College of Hydrology and Water Resources, Hohai University, No. 1 XiKang Road, Nanjing, Jiangsu 210098, China;Institute of Soft Matter Mechanics, Department of Engineering Mechanics, Hohai University, No. 1 XiKang Road, Nanjing, Jiangsu 210098, China
Venue:
Signal Processing
Year:
2013

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Abstract

Levy 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 Levy statistics. This article makes a survey on various numerical approaches available today to calculate statistical quantities of Levy stable distributions. And then based on this investigation, we introduce a new MATLAB toolbox, called LSD, to evaluate statistical quantities of Levy 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 Levy stable distributions.