Simulates n random vectors \(X\) exactly distributed
from the d-dimensional Student distribution with
df=\(\nu\) degrees of freedom, mean zero and scale matrix
sigma, conditional on \(l<X<u\),
tregress(n, lb, ub, sigma, df)
| n | number of observations |
|---|---|
| lb | vector of lower truncation limits |
| ub | vector of upper truncation limits |
| sigma | scale matrix |
| df | degrees of freedom |
list with components
R: n vector of scale
Z: a d by n matrix
so that \(\sqrt(\nu)Z/R\) follows a truncated Student distribution
Z. I. Botev and P. L'Ecuyer (2015), Efficient probability estimation and simulation of the truncated multivariate Student-t distribution, Proceedings of the 2015 Winter Simulation Conference, pp. 380-391,
d <- 5 tregress(lb =rep(-2, d), ub = rep(2, d), df = 3, n = 10, sigma = diag(0.5, d) + matrix(1, d, d))#> $R #> [1] 1.091621 1.985454 1.924308 2.038754 1.591299 1.729790 1.765749 1.735859 #> [9] 2.729171 1.778877 #> #> $Z #> [,1] [,2] [,3] [,4] [,5] #> [1,] -0.6758494 -0.4119034 -1.01023148 0.04240809 0.6892162 #> [2,] -1.2148716 -2.1112704 -1.33718004 -1.91212867 -1.5162984 #> [3,] -0.4317419 -0.4487589 0.35115041 -0.64842553 -0.2188923 #> [4,] 0.2261569 -0.2999287 -0.08212145 0.57409001 1.5177097 #> [5,] 1.2439582 -1.0904283 -1.44418026 -1.45235922 -0.2535841 #> [6,] -0.9776324 0.1335521 1.04890677 -1.65683327 1.0631266 #> [7,] -1.1206467 1.5654014 -0.21995049 0.44254103 1.4139640 #> [8,] -0.3793248 -1.1247627 0.82225738 -0.22067044 0.9058845 #> [9,] 0.4965089 -0.4627494 0.12161087 -0.63571020 0.8978638 #> [10,] 0.1621694 0.8973604 1.17407636 0.58679919 -0.8615315 #>