JSM 2005 - Toronto

Abstract #303992

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Legend: = Applied Session, = Theme Session, = Presenter
Activity Number: 325
Type: Contributed
Date/Time: Tuesday, August 9, 2005 : 2:00 PM to 3:50 PM
Sponsor: Section on Statistical Computing
Abstract - #303992
Title: A Method for Simulating Multivariate Nonnormal Distributions from the Generalized Lambda Distribution
Author(s): Todd C. Headrick*+ and Abdel Mugdadi
Companies: Southern Illinois University, Carbondale and Southern Illinois University, Carbondale
Address: 222J Wham Bldg Mail Code 4618 SIUC, Carbondale, IL, 62901-4618, United States
Keywords: Correlated Data ; Generalized Lambda Distribution ; Moments ; Monte Carlo ; Simulation
Abstract:

The Generalized Lambda Distribution (GLD) is used primarily for modeling univariate, real-world datasets. The GLD has not been as popular as other competing methods for simulating observations from multivariate nonnormal distributions with arbitrary correlation matrices because of computational complexities. In view of this, we develop a procedure for simulating multivariate nonnormal distributions from the GLD with an emphasis on increasing computational efficiency. The procedure is based on a derivation of the univariate GLD probability density function using the standard normal distribution as the basis of uniform random number generation. This derivation is subsequently extended to the multivariate case where intermediate correlations between standard normal distributions can be analytically determined. The intermediate correlations control for the nonnormalization effect of the GLD transformation such that the multivariate nonnormal distributions have their associated prespecified correlations. Numerical examples are worked and parametric plots of distributions are provided to demonstrate the methodology.

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