# rValeMaurelli: Generate non-normal data with Vale & Maurelli's (1983) method In SimDesign: Structure for Organizing Monte Carlo Simulation Designs

## Description

Generate multivariate non-normal distributions using the third-order polynomial method described by Vale & Maurelli (1983). If only a single variable is generated then this function is equivalent to the method described by Fleishman (1978).

## Usage

 ```1 2 3 4 5 6 7``` ```rValeMaurelli( n, mean = rep(0, nrow(sigma)), sigma = diag(length(mean)), skew = rep(0, nrow(sigma)), kurt = rep(0, nrow(sigma)) ) ```

## Arguments

 `n` number of samples to draw `mean` a vector of k elements for the mean of the variables `sigma` desired k x k covariance matrix between bivariate non-normal variables `skew` a vector of k elements for the skewness of the variables `kurt` a vector of k elements for the kurtosis of the variables

## Author(s)

Phil Chalmers rphilip.chalmers@gmail.com

## References

Chalmers, R. P., & Adkins, M. C. (2020). Writing Effective and Reliable Monte Carlo Simulations with the SimDesign Package. `The Quantitative Methods for Psychology, 16`(4), 248-280. doi: 10.20982/tqmp.16.4.p248

Sigal, M. J., & Chalmers, R. P. (2016). Play it again: Teaching statistics with Monte Carlo simulation. `Journal of Statistics Education, 24`(3), 136-156. doi: 10.1080/10691898.2016.1246953

Fleishman, A. I. (1978). A method for simulating non-normal distributions. Psychometrika, 43, 521-532.

Vale, C. & Maurelli, V. (1983). Simulating multivariate nonnormal distributions. Psychometrika, 48(3), 465-471.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18``` ```set.seed(1) # univariate with skew nonnormal <- rValeMaurelli(10000, mean=10, sigma=5, skew=1, kurt=3) # psych::describe(nonnormal) # multivariate with skew and kurtosis n <- 10000 r12 <- .4 r13 <- .9 r23 <- .1 cor <- matrix(c(1,r12,r13,r12,1,r23,r13,r23,1),3,3) sk <- c(1.5,1.5,0.5) ku <- c(3.75,3.5,0.5) nonnormal <- rValeMaurelli(n, sigma=cor, skew=sk, kurt=ku) # cor(nonnormal) # psych::describe(nonnormal) ```

SimDesign documentation built on Sept. 5, 2021, 5:23 p.m.