Energy test of equality of distributions using the alpha-transformation {Compositional}

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.

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.

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.

Author(s)

Michail Tsagris.

R implementation and documentation: Michail Tsagris [e-mail].

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

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) )