Truncated multivariate student cumulative distribution
Computes an estimator of the probability Pr(l<X<u),
where X is a centered multivariate student vector
with scale matrix Sig and degrees of freedom df.
Infinite values for vectors u and l are accepted.
mvTcdf(l, u, Sig, df, n = 1e+05)
l |
lower bound for truncation (infinite values allowed) |
u |
upper bound for truncation |
Sig |
covariance matrix |
df |
degrees of freedom |
n |
sample size |
Monte Carlo method uses sample size n; the larger
the n, the smaller the relative error of the estimator;
a list with components
prob: estimated value of probability Pr(l<X<u)
relErr: estimated relative error of estimator
upbnd: theoretical upper bound on true Pr(l<X<u)
If you want to estimate Pr(l<Y<u),
where Y follows a Student distribution with df degrees of freedom,
location vector m and scale matrix Sig,
then use mvTqmc(Sig, l - m, u - m, nu, n).
Matlab code by Zdravko Botev, R port by Leo Belzile
Z. I. Botev (2017), The Normal Law Under Linear Restrictions: Simulation and Estimation via Minimax Tilting, Journal of the Royal Statistical Society, Series B, 79 (1), pp. 1–24
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 <- 15; nu <- 30; l <- rep(2, d); u <- rep(Inf, d); Sig <- 0.5 * matrix(1, d, d) + 0.5 * diag(1, d); est <- mvTcdf(l, u, Sig, nu, n = 1e4) # mvtnorm::pmvt(lower = l, upper = u, df = nu, sigma = Sig) ## Not run: d <- 5 Sig <- solve(0.5*diag(d)+matrix(0.5, d,d)) # mvtnorm::pmvt(lower = rep(-1,d), upper = rep(Inf, d), df = 10, sigma = Sig)[1] mvTcdf(rep(-1, d), u = rep(Inf, d), Sig = Sig, df = 10, n=1e4)$prob ## End(Not run)
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