Author: Wen Qu and Zhiyong Zhang

# Introduction to mnonr

#### Wen Qu and Zhiyong Zhang

Non-normal data is everywhere. In order to test the influence of the non-normality on your model, you may what to generate some non-normal data first. The existing methods of generating multivariate non-normal data typically create data according to specific univariate marginal measures such as the univariate skewness and kurtosis, like the widely-used Vale and Maurelli’s method(Vale and Maurelli 1983), but not multivariate measures such as Mardia’s skewness and kurtosis (Mardia 1970). We create a new method of generating multivariate non-normal data with given multivariate skewness and kurtosis (Qu et al. 2019).

The goal of mnonr package is to give you a simple and quick way to generate multivariate non-normal data with pre-specified multivariate measures (skewness and kurtosis).

The package consists of three functions:

- mnonr: a function that can generate multivariate data with pre-specified multivariate skewness and kurtosis;

- unonr: a function that can generate multivariate data with pre-specified marginal skewness and kurtosis;

- mardia: a function that can check univariate and multivariate skewness and kurtosis.

The functions are easy to use. As for mnonr, along with multivariate skewness and kurtosis, you can also specify sample size, number of variables, covariance matrix, and initial start values. The initial start values of a vector with 3 numbers for polynomial coefficients’ (b,c,d) (the default setting is (0.9,0.4,0)) will yield different coefficient sets which could affect the multivariate skewness and kurtosis (more details are in the paper Qu et al. (2019)). We recommend that users should try with different start values in data simulation.

The unonr function is copied from mvrnonnorm function in the semTools package (Jorgensen et al. 2019).

The mardia can return the result of both marginal and multivariate skewness and kurtosis.

# Reference

Jorgensen, Terrence D., Sunthud Pornprasertmanit, Alexander M. Schoemann, and Yves Rosseel. 2019. `semTools`: Useful Tools for Structural Equation Modeling. https://CRAN.R-project.org/package=semTools.
Mardia, K. V. 1970. “Measures of Multivariate Skewness and Kurtosis with Applications.” Biometrika 57 (3): 519–30. https://doi.org/10.1093/biomet/57.3.519.
Qu, Wen, Haiyan Liu, and Zhiyong Zhang. 2019. “A Method of Generating Multivariate Non-Normal Random Numbers with Desired Multivariate Skewness and Kurtosis.” Behavior Research Methods, ahead of print. https://doi.org/10.3758/s13428-019-01291-5.
Vale, C. David, and Vincent A. Maurelli. 1983. “Simulating Multivariate Nonnormal Distributions.” Psychometrika 48 (3): 465–71. https://doi.org/10.1007/BF02293687.