dist.Multivariate.t: Multivariate t Distribution

Description Usage Arguments Details Value Author(s) See Also Examples

Description

These functions provide the density and random number generation for the multivariate t distribution, otherwise called the multivariate Student distribution.

Usage

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dmvt(x, mu, S, df=Inf, log=FALSE)
rmvt(n=1, mu, S, df=Inf)

Arguments

x

This is either a vector of length k or a matrix with a number of columns, k, equal to the number of columns in scale matrix S.

n

This is the number of random draws.

mu

This is a numeric vector or matrix representing the location parameter,mu (the mean vector), of the multivariate distribution (equal to the expected value when df > 1, otherwise represented as nu > 1). When a vector, it must be of length k, or must have k columns as a matrix, as defined above.

S

This is a k x k positive-definite scale matrix S, such that S*df/(df-2) is the variance-covariance matrix when df > 2. A vector of length 1 is also allowed (in this case, k=1 is set).

df

This is the degrees of freedom, and is often represented with nu.

log

Logical. If log=TRUE, then the logarithm of the density is returned.

Details

The multivariate t distribution, also called the multivariate Student or multivariate Student t distribution, is a multidimensional extension of the one-dimensional or univariate Student t distribution. A random vector is considered to be multivariate t-distributed if every linear combination of its components has a univariate Student t-distribution. This distribution has a mean parameter vector mu of length k, and a k x k scale matrix S, which must be positive-definite. When degrees of freedom nu=1, this is the multivariate Cauchy distribution.

Value

dmvt gives the density and rmvt generates random deviates.

Author(s)

Statisticat, LLC. [email protected]

See Also

dinvwishart, dmvc, dmvcp, dmvtp, dst, dstp, and dt.

Examples

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library(LaplacesDemonCpp)
x <- seq(-2,4,length=21)
y <- 2*x+10
z <- x+cos(y) 
mu <- c(1,12,2)
S <- matrix(c(1,2,0,2,5,0.5,0,0.5,3), 3, 3)
df <- 4
f <- dmvt(cbind(x,y,z), mu, S, df)
X <- rmvt(1000, c(0,1,2), S, 5)
joint.density.plot(X[,1], X[,2], color=TRUE)

LaplacesDemonR/LaplacesDemonCpp documentation built on May 9, 2017, 4:18 a.m.