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. Click here for more information. Note: the June 30, 2006 deadline has passed, but a limited number of grants may still be made. Note that decisions on grant applications will be based on plans for use of the STABLE program and for disseminating results.

Purchase STABLE online

The current version of STABLE sells for $200. It can be ordered online using a credit card. After your order is processed, we will ship the software to you by e-mail or regular mail. Credit card orders are usually shipped the next working day.

Version Windows platformLinux platform
matlab (view manual)

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


An Excel version and an α-stable signal processing toolbox for matlab are also Under development. For more information, use the contact page listed below.

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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