mvnorm.e {energy} | R Documentation |
Computes the E-statistic (energy statistic) for testing multivariate or univariate normality when parameters are estimated.
mvnorm.e(x)
x |
matrix or vector of sample data |
If x
is a matrix, each row is a multivariate observation. The
data will be standardized to zero mean and identity covariance matrix
using the sample mean vector and sample covariance matrix. If x
is a vector, the univariate statistic normal.e(x)
is returned.
If the data contains missing values or the sample covariance matrix is
singular, NA is returned.
The E-test of multivariate normality was proposed and implemented by Szekely and Rizzo (2004). The test statistic for d-variate normality is given by
E = n((2/n) sum[1:n] E||y_i-Z|| - E||Z-Z'|| - (1/n^2) sum[1:n,1:n] ||y_i-y_j||),
where y_1,...,y_n is the standardized sample, Z, Z' are iid standard d-variate normal, and || || denotes Euclidean norm.
The value of the E-statistic for multivariate (univariate) normality is returned.
Maria L. Rizzo rizzo@math.ohiou.edu and Gabor J. Szekely gabors@bgnet.bgsu.edu
Szekely, G. J. and Rizzo, M. L. (2004) A New Test for Multivariate Normality, Journal of Multivariate Analysis, http://dx.doi.org/10.1016/j.jmva.2003.12.002.
Rizzo, M. L. (2002). A New Rotation Invariant Goodness-of-Fit Test, Ph.D. dissertation, Bowling Green State University.
Szekely, G. J. (1989) Potential and Kinetic Energy in Statistics, Lecture Notes, Budapest Institute of Technology (Technical University).
## compute multivariate normality test statistic for iris Setosa data data(iris) mvnorm.e(iris[1:50, 1:4])