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 engineering, noise in some communications, radar and sonar systems is heavy tailed. In economics and finance, stable laws are used to model fluctuations of stocks prices and foreign exchange rates, compute Value At Risk, and model large insurance claims. They are used in hydrology to model super-diffusion of a fluid through an aquifer. 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 web page has more information about stable distributions and a free Windows programs for doing basic calculations 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, Excel, R, and Mathematica. All the capabilities of the free STABLE program are available, plus more features, at increased speed. The library has functions to compute stable densities, cumulative distribution functions, 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. Linear regression with stable error terms is now included.

New features include support for bivariate stable distributions: density calculations, cdf (probability of being in a rectangle), simulation and estimation of spectral measure. For higher dimensional data, the STABLE program supports isotropic and elliptically contoured stable distributions for up to 100 dimensions. For an isotropic/radially symmetric distribution X, the amplitude is defined by R=|X| (a generalized Rayleigh distribution). Functions are included to calculate the density and cumulative distribution of the amplitude distribution, as well as simulating samples from the amplitude distribution. For isotropic or elliptically contoured distributions, the program can fit data, compute densities, and simulate for dimension up to 100.

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, Excel, R, and Mathematica can be purchased below.

STABLE version 5.1 was released in January 2009. It is completely rewritten and now runs under both Windows and linux. In July 2009 we released the α-stable signal filtering toolbox for matlab. This toolbox implements nonlinear stable filters for filtering out spikey/impulsive/heavy tailed noise. The filters can be unweighted or weighted. In addition, signed weighted and matched filters are defined for the detection of waveforms, e.g. a chirp, in a noisy signal. In 2010, we added support for 64-bit linux and Excel.

Purchase STABLE online

The STABLE package can be ordered online using a credit card. All versions include the STABLE software, getting started instructions, a user manual, and scripts demonstrating how to use each function.

To order, look down the rows of the table below for the version you want. Note that for matlab, you can purchase just the STABLE core toolbox (first row), or you can purchase the combined STABLE core and the signal filtering (second row). Then go over to the ``Select platform'' column. On the next page, select the version of the software that you want: Windows, linux, or Mac. We now support 64 bit platforms. This will connect you to a secure server (esellerate.net) that will process your order and 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.

Note: these prices are for single user licenses. For other licensing arrangements, information about other environments, volume pricing (more than 2 copies), to order by mail, or other issues, use the contact page.


NOTE: Orders are not available immediately, so please be patient. When you place an order, it goes through a process to check your credit card. When that is approved, we get an e-mail informing us of your order, we build the software you requested, and we e-mail it to you. This usually occurs within one business day.

Version of STABLE cost* User Manual Buy now
Excel Add-on $100 STABLE for Excel Select platform
matlab STABLE toolbox (no signal filtering)
(matlab version 7.1 or above required)
                        MathWorks partner
$300 STABLE for matlab Select platform
matlab combined STABLE and signal filtering toolbox
(matlab version 7.1 or above required)
$500 STABLE and Signal
Filtering for matlab
Select platform
R $300 STABLE for R Select platform
Mathematica $300 STABLE for Mathematica Select platform
Stand-alone C library (binary) $300 STABLE for C Select platform
Prearranged software/consulting payments contact us   Select platform

* Prices are in US dollars. The company that handles our credit card sales will convert to other currencies. Tax will be added at checkout: U.S. customers will be charged the rate for their state; international customers will be charged appropriate VAT for their country.

Grant program

Note: this grant program is officially over, but a limited number of grants may still be made.

Academic and non-profit organizations may apply for a grant program that awards a limited number of free copies of STABLE. Decisions on grant applications will be based on concrete plans for use of the STABLE program and for disseminating results in publications, talks, etc. Click STABLE Software Grant Application for more information.

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, on a different platform, multi-user licenses, or other consulting work, please contact us using our contact page


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