R: The Multivariate t Distribution

Multivariate-t {nimble} | R Documentation

## 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, Σ^{-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)

[Package nimble version 0.9.1 Index]