Generate data with the multivariate t distribution

Function generates data from the multivariate t distribution given a covariance matrix, non-centrality parameter (or mode), and degrees of freedom.

Usage

rmvt(n, sigma, df, delta = rep(0, nrow(sigma)), Kshirsagar = FALSE)

Arguments

n: number of observations to generate
sigma: positive definite covariance matrix
df: degrees of freedom. df = 0 and df = Inf corresponds to the multivariate normal distribution
delta: the vector of non-centrality parameters of length n which specifies the either the modes (default) or non-centrality parameters
Kshirsagar: logical; triggers whether to generate data with non-centrality parameters or to adjust the simulated data to the mode of the distribution. The default uses the mode

Value

a numeric matrix with columns equal to ncol(sigma)

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

Author

Phil Chalmers rphilip.chalmers@gmail.com

Examples


# random t values given variances [3,6], covariance 2, and df = 15
sigma <- matrix(c(3,2,2,6), 2, 2)
x <- rmvt(1000, sigma = sigma, df = 15)
head(x)
#>            [,1]      [,2]
#> [1,]  1.1355823 -1.511125
#> [2,]  4.2293566  3.520368
#> [3,]  1.4742611 -2.296661
#> [4,]  0.4845494 -0.982761
#> [5,] -0.4792007 -3.010312
#> [6,] -1.8363903 -1.736213
summary(x)
#>        V1                 V2           
#>  Min.   :-6.15834   Min.   :-10.22541  
#>  1st Qu.:-1.27204   1st Qu.: -1.86951  
#>  Median :-0.06571   Median : -0.13726  
#>  Mean   :-0.05165   Mean   : -0.06365  
#>  3rd Qu.: 1.23916   3rd Qu.:  1.80329  
#>  Max.   : 8.84541   Max.   : 10.35493  
plot(x[,1], x[,2])