Want to create a vector in which multivariate skewness of the four multivariate normal populations can be stored

Minimum Working example:

library(Matrix)
library(psych)
library(MASS) 
set.seed(10)
N0 <- 1
n0 <- 5
p0 <- 2
q0 <- 4
n  <- n0*q0
m2 <- matrix(c(0, 0), p0, 1)
s2 <- matrix(c(1, 0, 0, 1), p0, p0)
mardia_lst <- list() 
for (i in 1:q0) {
  for (j in 1:N0) {
    Dat[, , j, i] <- mvrnorm(n=n0, m2, s2)
    mardia_lst[[i]] <- mardia(Dat[, , j, i], plot=FALSE)
  }
}
str(mardia_lst)

I want to store the multivariate skewness coefficients in mardia_lst.

When I run the program it only gives the multivariate skewness of one multivariate data set and other three are omitted. I want a vector that shows the multivariate skewness coefficients of all four.

The problem was that you were overwriting mardi_lst[[I]] with each iteration of j. You can make each [[I]] element of mardi_lst itself a list and then you will save all the values like this:

library(Matrix)
library(psych)
library(MASS) 
set.seed(10)
N0 <- 1
n0 <- 5
p0 <- 2
q0 <- 4
n  <- n0*q0
m2 <- matrix(c(0,0),p0,1)
s2 <- matrix(c(1,0,0,1),p0,p0)
Dat <- array(dim=c(n0, length(m2),  N0, q0))
mardia_lst <- vector(mode="list", length=q0)
for (i in 1:q0) {
  mardia_lst[[i]] <- vector(mode="list", length=N0)
  for (j in 1:N0) {
    Dat[,,j,i] <- MASS::mvrnorm(n = n0, m2, s2)
    mardia_lst[[i]][[j]] <- mardia(Dat[,,j,i], plot = FALSE)
  }
}
mardia_lst
#> [[1]]
#> [[1]][[1]]
#> Call: mardia(x = Dat[, , j, i], plot = FALSE)
#> 
#> Mardia tests of multivariate skew and kurtosis
#> Use describe(x) the to get univariate tests
#> n.obs = 5   num.vars =  2 
#> b1p =  0.78   skew =  0.65  with probability  <=  0.96
#>  small sample skew =  1.55  with probability <=  0.82
#> b2p =  3.08   kurtosis =  -1.38  with probability <=  0.17
#> 
#> [[2]]
#> [[2]][[1]]
#> Call: mardia(x = Dat[, , j, i], plot = FALSE)
#> 
#> Mardia tests of multivariate skew and kurtosis
#> Use describe(x) the to get univariate tests
#> n.obs = 5   num.vars =  2 
#> b1p =  1.17   skew =  0.97  with probability  <=  0.91
#>  small sample skew =  2.34  with probability <=  0.67
#> b2p =  3.56   kurtosis =  -1.24  with probability <=  0.21
#> 
#> [[3]]
#> [[3]][[1]]
#> Call: mardia(x = Dat[, , j, i], plot = FALSE)
#> 
#> Mardia tests of multivariate skew and kurtosis
#> Use describe(x) the to get univariate tests
#> n.obs = 5   num.vars =  2 
#> b1p =  0.17   skew =  0.14  with probability  <=  1
#>  small sample skew =  0.34  with probability <=  0.99
#> b2p =  2.95   kurtosis =  -1.41  with probability <=  0.16
#> 
#> [[4]]
#> [[4]][[1]]
#> Call: mardia(x = Dat[, , j, i], plot = FALSE)
#> 
#> Mardia tests of multivariate skew and kurtosis
#> Use describe(x) the to get univariate tests
#> n.obs = 5   num.vars =  2 
#> b1p =  1.12   skew =  0.93  with probability  <=  0.92
#>  small sample skew =  2.23  with probability <=  0.69
#> b2p =  3.35   kurtosis =  -1.3  with probability <=  0.19

^{Created on 2024-05-10 with reprex v2.0.2}