pmvt(lower, upper, df, corr, delta, maxpts=25000, abseps=0.001, releps=0)For a given correlation matrix corr, for short $A$, say,
(which has to be positive semi-definite) and
degrees of freedom df the following
values are numerically evaluated
$$I = K \int s^{df-1} \exp(-s^2/2) \Phi(s \cdot lower/\sqrt{df}-delta, s \cdot upper/\sqrt{df}-delta) ds$$
where $\Phi(a,b) = K^\prime \int_a^b \exp(-x^\prime Ax/2) dx$ is the multivariate normal distribution, $K^\prime = 1/\sqrt{det(A)(2\pi)^m}$ and $K = 2^{1-df/2} / Gamma(df/2)$ are constants and the (single) integral of $I$ goes from 0 to +Inf.
Note that both -Inf and +Inf may be specified in the lower and upper integral
limits. Randomized quasi-Monte Carlo methods are used for the computations.
Further information can be obtained from the quoted articles,
which can be downloaded (together with additional material
and additional codes) from the websites
Genz, A. and Bretz, F. (2001), Methods for the computation of multivariate t-probabilities. (submitted)
n <- 5
lower <- rep(-1, 5)
upper <- rep(3, 5)
df <- 4
corr <- diag(5)
corr[lower.tri(corr)] <- 0.5
delta <- rep(0, 5)
prob <- pmvt(lower, upper, df, corr , delta)
print(prob)Run the code above in your browser using DataLab