MomCumZabs: Moments and Cumulants of the Central Folded Normal...

In MultiStatM: Multivariate Statistical Methods

Moments and Cumulants of the Central Folded Normal Distribution

Description

Provides the theoretical moments and cumulants of the Central Folded Normal distribution. Depending on the choice of 'Type', either the univariate or d-variate distribution is used.

Usage

MomCumZabs(r, d, Type, nCum = FALSE)

Arguments

r	The highest moment (cumulant) order.
d	Integer; the dimension of the distribution. Must be 1 when 'Type' is "Univariate" and greater than 1 when 'Type' is "Multivariate".
Type	Character; specifies the type of distribution. Must be either "Univariate" or "Multivariate".
nCum	Logical; if TRUE, then cumulants are calculated.

Value

A list containing moments and optionally cumulants.

• For "Univariate" type:

  • MuZ: The moments of the univariate Central Folded Normal distribution.

  • CumZ: The cumulants of the univariate Central Folded Normal distribution.

• For "Multivariate" type:

  • MuZ: The moments of the d-variate Central Folded Normal distribution.

  • CumZ: The cumulants of the d-variate Central Folded Normal distribution.

References

Gy.Terdik, Multivariate statistical methods - Going beyond the linear, Springer 2021, Proposition 5.1 p.242 and formula: p. 301

See Also

Other Moments and cumulants: Cum2Mom(), EVSKSkewNorm(), EVSKUniS(), Mom2Cum(), MomCumCFUSN(), MomCumSkewNorm(), MomCumUniS()

Examples

# Univariate case: The first three moments
MomCumZabs(3, 1, Type = "Univariate")
# Univariate case: The first three moments and cumulants
MomCumZabs(3, 1, Type = "Univariate",nCum = TRUE)
# d-variate case: The first three moments
MomCumZabs(3, 2, Type = "Multivariate" )
# d-variate case: The first three moments and cumulants
MomCumZabs(3, d=2, Type = "Multivariate",  nCum = TRUE)

MultiStatM documentation built on Sept. 11, 2024, 6:01 p.m.