pmvt {TruncatedNormal} | R Documentation |
Distribution function of the multivariate Student distribution for arbitrary limits
Description
This function computes the distribution function of a multivariate normal distribution vector for an arbitrary rectangular region [lb
, ub
].
pmvt
computes an estimate and the value is returned along with a relative error and a deterministic upper bound of the distribution function of the multivariate normal distribution.
Infinite values for vectors u
and l
are accepted. The Monte Carlo method uses sample size n
: the larger the sample size, the smaller the relative error of the estimator.
Usage
pmvt(
mu,
sigma,
df,
lb = -Inf,
ub = Inf,
type = c("mc", "qmc"),
B = 10000,
check = TRUE,
...
)
Arguments
mu |
vector of location parameters |
sigma |
scale matrix |
df |
degrees of freedom |
lb |
vector of lower truncation limits |
ub |
vector of upper truncation limits |
type |
string, either of |
B |
number of replications for the (quasi)-Monte Carlo scheme |
check |
logical, if |
... |
additional arguments, currently ignored. |
Author(s)
Matlab
code by Zdravko I. Botev, R
port by Leo Belzile
References
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
Examples
d <- 15; nu <- 30;
l <- rep(2, d); u <- rep(Inf, d);
sigma <- 0.5 * matrix(1, d, d) + 0.5 * diag(1, d);
est <- pmvt(lb = l, ub = u, sigma = sigma, df = nu)
# mvtnorm::pmvt(lower = l, upper = u, df = nu, sigma = sigma)
## Not run:
d <- 5
sigma <- solve(0.5 * diag(d) + matrix(0.5, d, d))
# mvtnorm::pmvt(lower = rep(-1,d), upper = rep(Inf, d), df = 10, sigma = sigma)[1]
pmvt(lb = rep(-1, d), ub = rep(Inf, d), sigma = sigma, df = 10)
## End(Not run)