IntGramCharlier

Computes the integrals of the \(d\)-variate Gram Charlier density
with respect to the normal density
It integrates the <code>GramCharlier</code> with the first 4
cumulants.

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

IntGramCharlier function

<dl><dt>x</dt>
<dd>An nxd data matrix</dd>
<dt>cum</dt>
<dd>Unstandardized first four cumlants</dd>
<dt>type</dt>
<dd>Character string specifying the integration range.
Must be one of:<ul>
<li><code>"lower"</code>: integrate from \(-\infty\) to \(x\)</li>
<li><code>"upper"</code>: integrate from \(x\) to \(+\infty\)</li>
</ul></dd></dl>

Arguments

Integrate Gram Charlier density — IntGramCharlier

<dl>

<dt>x</dt>
<dd>An nxd data matrix</dd>


<dt>cum</dt>
<dd>Unstandardized first four cumlants</dd>


<dt>type</dt>
<dd>Character string specifying the integration range.
Must be one of:<ul>
<li><code>"lower"</code>: integrate from \(-\infty\) to \(x\)</li>
<li><code>"upper"</code>: integrate from \(x\) to \(+\infty\)</li>
</ul></dd>

</dl>

IntGramCharlier: Integrate Gram Charlier density

Description

Usage

Value

Arguments

See Also

Examples