# MVNMIX: Random Generation for the Normal Mixture Distribution In mvnormalTest: Powerful Tests for Multivariate Normality

## Description

Generate univariate or multivariate random sample for the normal mixture distribution with density λ N(0,∑_1)+(1-λ)N(bl, ∑_2), where l is the column vector with all elements being 1, ∑_i=(1-ρ_i)I+ρ_ill^T for i=1,2. ρ has to satisfy ρ > -1/(p-1) in order to make the covariance matrix meaningful.

## Usage

 `1` ```MVNMIX(n, p, lambda, mu2, rho1 = 0, rho2 = 0) ```

## Arguments

 `n` number of rows (observations). `p` total number of columns (variables). `lambda` weight parameter to allocate the proportions of the mixture, 0<λ<1. `mu2` is bl of N(bl, ∑_2). `rho1` parameter in ∑_1. `rho2` parameter in ∑_2.

## Value

Returns univariate (p=1) or multivariate (p>1) random sample matrix.

## References

Zhou, M., & Shao, Y. (2014). A powerful test for multivariate normality. Journal of applied statistics, 41(2), 351-363.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11``` ```set.seed(12345) ## Generate 5X2 random sample matrix from MVNMIX(0.5,4,0,0) ## MVNMIX(n=5, p=2, lambda=0.5, mu2=4, rho1=0, rho2=0) ## Power calculation against bivariate (p=2) MVNMIX(0.5,4,0,0) distribution ## ## at sample size n=50 at one-sided alpha = 0.05 ## # Zhou-Shao's test # power.mvnTest(a=0.05, n=50, p=2, B=100, FUN=MVNMIX, lambda=0.5, mu2=4, rho1=0, rho2=0) ```

mvnormalTest documentation built on April 28, 2020, 5:06 p.m.