MomCumMVt

The t- distribution is defined as
$$\mathbf{X} = \sqrt{\frac{p}{S^2}} \mathbf{Z}$$
where $\mathbf{Z}$ is a multivariate standard-normal random vector
and $S^2$ is a $\chi^2_p$.
random variable independent of $\mathbf{Z}$.

Algorithms to build set partitions and commutator matrices and their use in the
construction of multivariate d-Hermite polynomials;  estimation and derivation of theoretical  vector moments and vector
cumulants  of multivariate distributions; conversion formulae for multivariate moments and cumulants. Applications to
estimation and derivation of multivariate measures of skewness and kurtosis;  estimation and derivation of asymptotic
covariances for d-variate Hermite polynomials, multivariate moments and cumulants and measures of skewness and kurtosis.
The formulae implemented are discussed in Terdik (2021, ISBN:9783030813925), "Multivariate Statistical Methods".

Emanuele Taufer

MultiStatM

Multivariate Statistical Methods

Gyorgy Terdik

MomCumMVt function

<dl><dt>p</dt>
<dd>degrees of freedom</dd>
<dt>d</dt>
<dd>dimension</dd>
<dt>r</dt>
<dd>highest order of moments and cumulants</dd>
<dt>nCum</dt>
<dd>if it is TRUE then cumulants are calculated</dd></dl>

Arguments

Moments and cumulants Multivariate t-Student distribution — MomCumMVt

<dl>

<dt>p</dt>
<dd>degrees of freedom</dd>


<dt>d</dt>
<dd>dimension</dd>


<dt>r</dt>
<dd>highest order of moments and cumulants</dd>


<dt>nCum</dt>
<dd>if it is TRUE then cumulants are calculated</dd>

</dl>

MomCumMVt: Moments and cumulants Multivariate t-Student distribution

Description

Usage

Value

Arguments

References

See Also

Examples