Fast fifth-order polynomial transforms for generating univariate and multivariate nonnormal distributions

Authors:
Todd C. Headrick
Affiliations:
Department of Measurement and Statistics, Southern Illinois University, 222-J, Wham Bldg., Mail 4618, Carbondale, IL
Venue:
Computational Statistics & Data Analysis
Year:
2002

Citing 4
Cited 1

Multivariate statistical simulation

Multivariate statistical simulation
Kendall's advanced theory of statistics

Kendall's advanced theory of statistics
The Mathematica book (4th edition)

The Mathematica book (4th edition)
An approximate method for generating asymmetric random variables

Communications of the ACM

Cressie and Read power-divergences as influence measures for logistic regression models

Computational Statistics & Data Analysis

Quantified Score

Hi-index	0.03

Visualization

Abstract

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.