Robust Analysis Inc


Robust Analysis, Inc. is a consulting and software company that specializes in analyzing problems that involve heavy tailed distributions. Our initial focus has been on stable distributions, a class of probability distributions that generalize normal distributions and allow heavy tails and skewness.

This rich class of probability distributions can model data in a wide range of applications. In economics and finance, they are being used to model fluctuations of stocks prices and foreign exchange rates. They are used in hydrology to model super-diffusion of a fluid through an aquifier. In engineering, noise in some communications and radar systems is heavy tailed. Also some network traffic quantities, e.g. file size of downloads, are heavy tailed.

Graph of stable densities

Stable densities computed with the STABLE program.
The values of α are indicated on the plots, skewness is indicated by color:
β=0 (black), β=0.25 (red), β=0.5 (green), β=0.75 (yellow), β=1 (blue).




Basic information on stable distributions

Basic facts about stable distributions can be found in an introduction to stable distributions (PDF format, 360 kb). This is a draft version of Chapter 1 in a forthcoming book on stable distributions. It describes one dimensional stable distributions in a non-technical way, explaining the two main parameterizations of stable laws.

John Nolan's academic webpage has more information about stable distributions and free Windows programs for working with stable distributions.


STABLE library and interfaces

We have developed a library of STABLE functions for programmers to call directly (from C, Fortran, or Visual Basic) and interfaces for matlab, S-Plus, R, and Mathematica. All the capabilities of the STABLE program are available, plus more features, at increased speed. The library has entry points to compute stable densities, cumulative distribution function, quantiles, hazard function, etc. at an arbitrary vector of values. It will estimate stable parameters by six methods: quantile method, empirical characteristic function method, numerical maximum likelihood estimation, fractional moments, log absolute moment, and modified quantile.

New features include support for bivariate stable distributions: density calculations, cdf (probability of being in a rectangle), simulation and estimation of spectral measure. For an isotropic/radially symmetric distribution X, the amplitude is defined by R=|X|. Functions are included to calculate the density and cumulative distribution of the amplitude distribution, as well as simulating samples from the amplitude distribution.

The user manual contains a description of all the functions, see online versions below. Here is a one page Power Point information sheet on STABLE. This library and/or interfaces for matlab, S-Plus, R, and Mathematica can be purchased below.

Grant program

Academic and non-profit organizations may apply for a grant program that awards a limited number of free copies of STABLE. Note: this grant program is officially over, but a limited number of grants may still be made. Note that decisions on grant applications will be based on concrete plans for use of the STABLE program and for disseminating results. Click here for more information.

Purchase STABLE online

In January 2009 we released a new version, STABLE 5.1. The price is still $200. (Note: the price has not changed since 2002. Due to increased expenses, the price will increase to $300 in July 2009.)

The STABLE package can be ordered online using a credit card. After you place your order, it will be processed by a secure service, who will verify your credit card. After that is done, they will send us your order and we will ship the software to you by e-mail. Credit card orders are usually shipped the next working day.

Version 32 bit Windows platform32 bit Linux platform
matlab (version 7.1 or above) (view manual)

      MathWorks partner
Buy Now at Reg.Net Under development
R (view manual) Buy Now at Reg.Net Under development
Mathematica (view manual) Buy Now at Reg.Net Under development
Stand-alone library (view manual) DLL for Windows
Buy Now at Reg.Net
Under development


We have limited support for the standalone library as a .so for 32-bit and 64-bit linux.

An Excel add-on is planned for the future.

For more information about these or other environments, use the contact page listed below.


STABLE signal filtering toolbox

An α-stable signal processing toolbox for matlab has been developed and is being tested. This toolbox provides robust non-linear filters based on stable models for impulsive, heavy tailed noise. This matlab toolbox is now planned for release on July 10, 2009. The price for the combined toolbox (STABLE and stable signal processing) will be $500. If you already have the STABLE toolbox for matlab, you can upgrade to the α-stable signal processing toolbox for $300.

You can see the new functions in sections 5 and 6 of the user manual: view new manual.

Mail orders

To order by mail, download an order form and follow instructions 

More information, other platforms and consulting

If you have any questions about the above products, are interested in a custom interface for STABLE to a different program or on a different platform, or other consulting work, please contact us using our contact page


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