aeqdist.etest: Energy test of equality of distributions using the... In Compositional: Compositional Data Analysis

 Energy test of equality of distributions using the alpha-transformation R Documentation

Energy test of equality of distributions using the α-transformation

Description

Energy test of equality of distributions using the α-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 α=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 α. `R` The number of permutations to apply in order to compute the approximate p-value.

Details

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

Value

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

Author(s)

Michail Tsagris.

R implementation and documentation: Michail Tsagris mtsagris@uoc.gr.

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

```acor, acor.tune, alfa, alfa.profile ```
```y <- rdiri(50, c(3, 4, 5) )