Multivariate_CGF_PLot: Graphical plots to assess multivariate normality assumption.

In PlotNormTest: Graphical Univariate/Multivariate Assessments for Normality Assumption

Graphical plots to assess multivariate normality assumption.

Description

Cumulant generating functions of normally distributed random variables has derivatives of order higher than 3 are all 0. Hence, plots of empirical third/fourth order derivatives with large value or high slope gives indication of non-normality. Multivariate_CGF_PLot estimates and provides confidence region for average (or any linear combination) of third/fourth derivatives of empirical cumulant function at the points t = t^*1_p. Plots for p = 2, 3, \dots, 10 will be faster to obtain, as confidence regions and other necessary parameters are available in mt3_lst_param.rda and mt4_lst_param.rda. Higher dimension requires expensive computational cost.

Usage

d3hCGF_plot(x, alpha = 0.05)

d4hCGF_plot(x, alpha = 0.05)

Arguments

x	Data matrix of size n \times p
alpha	Significant level (default is .05)

Value

d3hCGF_plot returns plot relying in third derivatives.

d4hCGF_plot returns plot relying in forth derivatives.

See Also

dhCGF_plot1D()

Examples

set.seed(1234)
p <- 3
x <- MASS::mvrnorm(500, rep(0, p), diag(p))
d3hCGF_plot(x)
d4hCGF_plot(x)

PlotNormTest documentation built on April 12, 2025, 9:14 a.m.