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