Description Usage Arguments Details Value Author(s) See Also Examples
These functions provide the density and random number generation for the multivariate t distribution, otherwise called the multivariate Student distribution.
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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 |
S |
This is a k x k positive-definite scale
matrix S, such that |
df |
This is the degrees of freedom, and is often represented with nu. |
log |
Logical. If |
Application: Continuous Multivariate
Density:
p(theta) = Gamma[(nu+k)/2] / {Gamma(nu/2)nu^(k/2)pi^(k/2)|Sigma|^(1/2)[1 + (1/nu)(theta-mu)^T*Sigma^(-1)(theta-mu)]^[(nu+k)/2]}
Inventor: Unknown (to me, anyway)
Notation 1: theta ~ t[k](mu, Sigma, nu)
Notation 2: p(theta) = t[k](theta | mu, Sigma, nu)
Parameter 1: location vector mu
Parameter 2: positive-definite k x k scale matrix Sigma
Parameter 3: degrees of freedom nu > 0 (df in the functions)
Mean: E(theta) = mu, for nu > 1, otherwise undefined
Variance: var(theta) = (nu / (nu - 2))*Sigma, for nu > 2
Mode: mode(theta) = mu
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.
dmvt
gives the density and
rmvt
generates random deviates.
Statisticat, LLC. software@bayesian-inference.com
dinvwishart
,
dmvc
,
dmvcp
,
dmvtp
,
dst
,
dstp
, and
dt
.
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