9873

Stable Distribution Function

The simple algorithm used in this Demonstration can calculate the stable distribution function and its first several derivatives with good accuracy for . It is offered to help with financial analysis where the data generally has the shape parameter greater than 1. The Nolan 1-parameterization is used where the parameters have the characteristics listed below.
is the distribution shape parameter, . For the result is the normal distribution; is the tail exponent of the distribution: lower values give fatter tails.
is the skewness parameter in the range (-1, 1).
is the scale parameter.
is the location parameter; when as in this Demonstration is the expectation of the distribution.

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

DETAILS

The speed of the algorithm may be considerably enhanced for the density and distribution functions by implementing each derivative separately and using only the real component of the integrand. For example the code samples below give the integrands for the distribution function, followed by the density function for .
NIntegrate in recent versions of Mathematica can handle this integrand quite well. Be sure to set: Method -> {Automatic, "SymbolicProcessing" -> 0}.
For many applications in finance and software for stable distributions visit mathestate.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.









 
RELATED RESOURCES
Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2014 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+