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Zbl 1103.65302
Headrick, Todd C.
Fast fifth-order polynomial transforms for generating univariate and multivariate nonnormal distributions. (English)
[J] Comput. Stat. Data Anal. 40, No. 4, 685-711 (2002). ISSN 0167-9473

Summary: A general procedure is derived for simulating univariate and multivariate nonnormal distributions using polynomial transformations of order five. The procedure allows for the additional control of the fifth and sixth moments. The ability to control higher moments increases the precision in the approximations of nonnormal distributions and lowers the skew and kurtosis boundary relative to the competing procedures considered. Tabled values of constants are provided for approximating various probability density functions. A numerical example is worked to demonstrate the multivariate procedure. The results of a Monte Carlo simulation are provided to demonstrate that the procedure generates specified population parameters and intercorrelations.

MSC 2000:: *65C10 Random number generation
65C60 Computational problems in statistics
65C05 Monte Carlo methods
62E99 Statistical distribution theory

Keywords: Correlated data; Cumulants; Moments; Nonnormal distributions; Simulation

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