IntHermiteN

Computes the integrals of d-Hermite polynomial with respect to the normal density
$$\int_{-\infty }^{\mathbf{y}}\mathbf{H}_{k-1}\left( \mathbf{s}\right) \varphi
\left( \mathbf{s}\right) d \,\mathbf{s}$$
either from $-\infty$ to $\mathbf{y}$ (type = "lower")
or from $\mathbf{y}$ to $+\infty$ ( type = "upper").

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

IntHermiteN function

<dl><dt>x</dt>
<dd>Numeric vector of lenght $d$</dd>
<dt>K</dt>
<dd>Integer. The order of the Hermite polynomial + 1.</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

IntHermiteN — IntHermiteN

<dl>

<dt>x</dt>
<dd>Numeric vector of lenght $d$</dd>


<dt>K</dt>
<dd>Integer. The order of the Hermite polynomial + 1.</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>

IntHermiteN: IntHermiteN

Description

Usage

Value

Arguments

Examples