Compositional (version 5.5)

Energy test of equality of distributions using the alpha-transformation: Energy test of equality of distributions using the \(\alpha\)-transformation

Description

Energy test of equality of distributions using the \(\alpha\)-transformation.

Usage

aeqdist.etest(x, sizes, a = 1, R = 999)

Arguments

x

A matrix with the compositional data with all groups stacked one under the other.

sizes

A numeric vector matrix with the sample sizes.

a

The value of the power transformation, it has to be between -1 and 1. If zero values are present it has to be greater than 0. If \(\alpha=0\) the isometric log-ratio transformation is applied. If more than one values are supplied the energy distance of equality of distributions is applied for each value of \(\alpha\).

R

The number of permutations to apply in order to compute the approximate p-value.

Value

A numerical value or a numerical vector, depending on the length of the values of \(\alpha\), with the approximate p-value(s) of the energy test.

Details

The \(\alpha\)-transformation is applied to each composition and then the energy distance of equality of distributions is applied for each value of \(\alpha\) or for the single value of \(\alpha\).

References

Szekely, G. J. and Rizzo, M. L. (2004) Testing for Equal Distributions in High Dimension. InterStat, November (5).

Szekely, G. J. (2000) Technical Report 03-05: E-statistics: Energy of Statistical Samples. Department of Mathematics and Statistics, Bowling Green State University.

Tsagris M.T., Preston S. and Wood A.T.A. (2011). A data-based power transformation for compositional data. In Proceedings of the 4th Compositional Data Analysis Workshop, Girona, Spain. https://arxiv.org/pdf/1106.1451.pdf

See Also

acor, acor.tune, alfa, alfa.profile

Examples

# NOT RUN {
y <- rdiri(50, c(3, 4, 5) )
x <- rdiri(60, c(3, 4, 5) )
aeqdist.etest( rbind(x, y), c(dim(x)[1], dim(y)[1]), a = c(-1, 0, 1) )
# }