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 |

`n` |
This is the number of random draws. |

`mu` |
This is a numeric vector or matrix representing the location
parameter, |

`S` |
This is a |

`df` |
This is the degrees of freedom, and is often represented
with |

`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 undefinedVariance:

*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. [email protected]

`dinvwishart`

,
`dmvc`

,
`dmvcp`

,
`dmvtp`

,
`dst`

,
`dstp`

, and
`dt`

.

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