tmvt: Multivariate truncated Student distribution

In lbelzile/TruncatedNormal: Truncated Multivariate Normal and Student Distributions

Multivariate truncated Student distribution

Description

Density, distribution function and random generation for the multivariate truncated Student distribution with location vector mu, scale matrix sigma, lower truncation limit lb, upper truncation limit ub and degrees of freedom df.

Arguments

n	number of observations
x, q	vector or matrix of quantiles
B	number of replications for the (quasi)-Monte Carlo scheme
log	logical; if TRUE, probabilities and density are given on the log scale.
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 mc or qmc for Monte Carlo and quasi Monte Carlo, respectively
check	logical, if TRUE (default), check that the scale matrix sigma is positive definite and symmetric.
...	additional arguments, currently ignored

Details

The truncation limits can include infinite values. The Monte Carlo (type = "mc") uses a sample of size B, while the qausi Monte Carlo (type = "qmc") uses a pointset of size ceiling(n/12) and estimates the relative error using 12 independent randomized QMC estimators.

pmvt computes an estimate 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 n, the smaller the relative error of the estimator.

Value

dtmvt gives the density, ptmvt gives the distribution function, rtmvt generate random deviates.

Usage

dtmvt(x, mu, sigma, df, lb, ub, type = c("mc", "qmc"), log = FALSE, B = 1e4)
ptmvt(q, mu, sigma, df, lb, ub, type = c("mc", "qmc"), log = FALSE, B = 1e4)
rtmvt(n, mu, sigma, df, lb, ub)
pmvt(mu, sigma, df, lb = -Inf, ub = Inf, type = c("mc", "qmc"), B = 1e4)

Author(s)

Leo Belzile, R port from Matlab code by Z. I. Botev

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 <- 4; lb <- rep(0, d)
mu <- runif(d)
sigma <- matrix(0.5, d, d) + diag(0.5, d)
samp <- rtmvt(n = 10, mu = mu, sigma = sigma, df = 2, lb = lb)
loglik <- dtmvt(samp, mu = mu, sigma = sigma, df = 2, lb = lb, log = TRUE)
cdf <- ptmvt(samp, mu = mu, sigma = sigma, df = 2, lb = lb, log = TRUE, type = "q")

lbelzile/TruncatedNormal documentation built on March 4, 2024, 5:50 p.m.