MultiStatM (version 2.0.0)

MomCumZabs: 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)

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.

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.

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)