Esti_Gram_Charlier {MultiStatM}

Gram-Charlier approximation to a multivariate density

Description

Provides the truncated Gram-Charlier approximation to a multivariate density. Approximation can be up to the first k=8 cumulants.

Usage

Esti_Gram_Charlier(X, k = 4, cum = NULL)

Arguments

X

A matrix of d-variate data

k

the order of the approximation, by default set to 4; (k must not be smaller than 3 or greater than 8)

cum

if NULL (default) the cumulant vector is estimated from X. If cum is provided no estimation of cumulants is performed.

Value

The vector of the Gram-Charlier density evaluated at X

References

Gy.Terdik, Multivariate statistical methods - Going beyond the linear, Springer 2021. Section 4.7.

Examples

# Gram-Charlier density approximation (k=4) of data generated from 
# a bivariate skew-gaussian distribution
n<-50
alpha<-c(10,0)
omega<-diag(2)
X<-distr_SkewNorm_Rand(n,omega,alpha)
EC<-Esti_EVSK(X)
fy4<-Esti_Gram_Charlier(X[1:5,],cum=EC)