PlotNormTest (version 1.0.1)

Multivariate_CGF_PLot: 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)

Value

d3hCGF_plot returns plot relying in third derivatives.

d4hCGF_plot returns plot relying in forth derivatives.

Arguments

x

Data matrix of size \(n \times p\)

alpha

Significant level (default is \(.05\))

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)