Finding Mardia's multivariate kurtosis
Finding Mardia's multivariate kurtosis of multiple variables
mardiaKurtosis(dat, use = "everything")
dat |
The target matrix or data frame with multiple variables |
use |
Missing data handling method from the |
The Mardia's multivariate kurtosis formula (Mardia, 1970) is
b_{2, d} = \frac{1}{n}∑^n_{i=1}≤ft[ ≤ft(\bold{X}_i - \bold{\bar{X}} \right)^{'} \bold{S}^{-1} ≤ft(\bold{X}_i - \bold{\bar{X}} \right) \right]^2,
where d is the number of variables, X is the target dataset with multiple variables, n is the sample size, \bold{S} is the sample covariance matrix of the target dataset, and \bold{\bar{X}} is the mean vectors of the target dataset binded in n rows. When the population multivariate kurtosis is normal, the b_{2,d} is asymptotically distributed as normal distribution with the mean of d(d + 2) and variance of 8d(d + 2)/n.
A value of a Mardia's multivariate kurtosis with a test statistic
Sunthud Pornprasertmanit (psunthud@gmail.com)
Mardia, K. V. (1970). Measures of multivariate skewness and kurtosis with applications. Biometrika, 57(3), 519–530. doi: 10.2307/2334770
skew Find the univariate skewness of a variable
kurtosis Find the univariate excessive kurtosis
of a variable
mardiaSkew Find the Mardia's multivariate skewness
of a set of variables
library(lavaan)
mardiaKurtosis(HolzingerSwineford1939[ , paste0("x", 1:9)])Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.