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Distributional Alchemy

William T. Shaw
Organization: King's College, University of London
Department: Department of Mathematics
URL: http://www.mth.kcl.ac.uk/staff/w_shaw.html

This pair of articles looks at converting one probability distribution into another by using the composition of a cumulative distribution function with a quantile function. There are several applications, notably:
  • Converting samples from one distribution into another for Monte Carlo sampling calculations;
  • Defining skew versions of standard distributions;
  • Introducing kurtosis into a standard distribution.
There is a formal mathematical paper, and a Mathematica notebook of a talk given at the Sydney QMF06 meeting in December 2006. Related work can be found at:

*Applied Mathematics > Computer Science
*Business and Economics
*Education > College
*Education > Graduate
*Mathematics > Calculus and Analysis > Series
*Mathematics > Calculus and Analysis > Special Functions
*Mathematics > Probability and Statistics
*Social Science > Sociology and Psychology
*Wolfram Technology > Programming > Equation Solving

Distributional Alchemy, Gram Charlier, Cornish Fisher, Skew Uniform, Skew Normal, Skew T, Skew Student, Student Distribution, T Distribution, Kurtotic Uniform, Kurtotic Normal, Skew Exponential

Downloads Download Wolfram CDF Player

alchemy.pdf (370.6 KB) - PDF Document
ShawQMF06ConfSite.nb (361.5 KB) - Mathematica Notebook [for Mathematica 5.2]