Multivariate-t: The Multivariate t Distribution

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The Multivariate t Distribution

Description

Density and random generation for the multivariate t distribution, using the Cholesky factor of either the precision matrix (i.e., inverse scale matrix) or the scale matrix.

Usage

dmvt_chol(x, mu, cholesky, df, prec_param = TRUE, log = FALSE)

rmvt_chol(n = 1, mu, cholesky, df, prec_param = TRUE)

Arguments

x	vector of values.
mu	vector of values giving the location of the distribution.
cholesky	upper-triangular Cholesky factor of either the precision matrix (i.e., inverse scale matrix) (when prec_param is TRUE) or scale matrix (otherwise).
df	degrees of freedom.
prec_param	logical; if TRUE the Cholesky factor is that of the precision matrix; otherwise, of the scale matrix.
log	logical; if TRUE, probability density is returned on the log scale.
n	number of observations (only n=1 is handled currently).

Details

See Gelman et al., Appendix A or the BUGS manual for mathematical details. The 'precision' matrix as used here is defined as the inverse of the scale matrix, \Sigma^{-1}, given in Gelman et al.

Value

dmvt_chol gives the density and rmvt_chol generates random deviates.

Author(s)

Peter Sujan

References

Gelman, A., Carlin, J.B., Stern, H.S., and Rubin, D.B. (2004) Bayesian Data Analysis, 2nd ed. Chapman and Hall/CRC.

See Also

Distributions for other standard distributions

Examples

mu <- c(-10, 0, 10)
scalemat <- matrix(c(1, .9, .3, .9, 1, -0.1, .3, -0.1, 1), 3)
ch <- chol(scalemat)
x <- rmvt_chol(1, mu, ch, df = 1, prec_param = FALSE)
dmvt_chol(x, mu, ch, df = 1, prec_param = FALSE)

nimble documentation built on Sept. 11, 2024, 7:10 p.m.