normal.e {energy}R Documentation

E-statistic (Energy Statistic) for Testing Univariate Normality

Description

Computes the E-statistic for testing univariate normality when parameters are estimated.

Usage

normal.e(x)

Arguments

x vector of univariate sample data

Details

The data will be standardized to zero mean and unit variance using the sample mean and sample variance. If the data contains missing values or the sample variance is zero, NA is returned.

The E-test of multivariate (and univariate) normality was proposed and implemented by Szekely and Rizzo (2004). The univariate test statistic is given by

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 and Z, Z' are iid standard normal variables. See mvnorm.e for the multivariate statistic.

Value

The value of the E-statistic for univariate normality is returned.

Author(s)

Maria Rizzo rizzo@math.ohiou.edu

References

Szekely, G. J. and Rizzo, M. L. (2004) A New Test for Multivariate Normality, Journal of Multivariate Analysis, to appear.

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).

See Also

mvnorm.e mvnorm.etest

Examples

 x <- rnorm(30)
 normal.e(x)

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