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Orthogonal Series Representations of Probability Density and Distribution Functions

J. Todd Reinking
Organization: Mission Research Corporation
Journal / Anthology

The Mathematica Journal
Year: 2002
Volume: 8
Issue: 3
Page range: 473-483

Introduction | General Orthogonal Series Representation | Three Specific Orthogonal Series Representations | Code Samples | Package Usage | Conclusion

When justified, moment methods may be used to evaluate probability density and distribution functions. These methods are particularly useful when moments are the only available information on the random variable of interest. A classic example of the technique considered here is the Gram-Charlier series representation of a probability density function. This paper provides a package to obtain three different orthogonal series expansions of a probability density function given a user-supplied function for moments. The three orthogonal series representations are based on Hermite (which gives the Gram-Charlier series), Laguerre, and Jacobi orthogonal polynomials and their corresponding weight functions.

*Mathematics > Calculus and Analysis > Series
*Mathematics > Probability and Statistics