Hi Mohit.

as far as I know Levy distribution is a more general distribution family which includes gaussian, exponential and power law distribution as particular cases. I am not an expert but in the attached links you can find two relevant applications, at least in economics.

I hope this could be somewhat useful for you.

Best

Ruggero

http://www.sciencedirect.com/science/article/pii/S0167268104001659

The second attachment

http://sage.math.washington.edu/home/wstein/www/home/simuw/simuw08/refs/fractal/mandelbrot-the_pareto_levy_law_and_the_distribution_of_income.pdf

A distribution does not fail...

You can make a histogram of your observations, and then see how the variability is distributed OR you have a theoretical model of how the variability should be distributed.

http://en.wikipedia.org/wiki/L%C3%A9vy_distribution

The Levy distribution is useful in modelling certain processes whose values are strictly not negative and which can change appreciably over the short term (Levy has a "heavy tail"). Both of these attributes are "non-Gaussian". For example, Levy is frequently used to model stock value in the market: stocks can be worthless, but not negative, and their value might change significantly in the short term. There are also some interesting technical properties, like its relationship to the Gaussian using a transformation.

Thanks a lot, Rigerro, Lambert and Michael.

Here you have, more or less exhaustive answer for your question:

http://arxiv.org/abs/math-ph/0106003

You will also find there a proposed implementation (in FORTRAN), very short, nearly one-liner. In addition, the description of a distribution in question given there is more general than the one given in Wikipedia:

http://en.wikipedia.org/wiki/Levy_distribution

Happy computing!

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