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.
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.
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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