acomparith: Power transform in the simplex

Description

The Aitchison Simplex with its two operations perturbation as + and power transform as * is a vector space. This vector space is represented by these operations.

Usage

power.acomp(x,s)
## Methods for class "acomp"
## x*y
## x/y

Value

An "acomp" vector or matrix.

Arguments

x: an acomp composition or dataset of compositions (or a number or a numeric vector)
y: a numeric vector of size 1 or nrow(x)
s: a numeric vector of size 1 or nrow(x)

Author

K.Gerald v.d. Boogaart http://www.stat.boogaart.de

Details

The power transform is the basic multiplication operation of the Aitchison simplex seen as a vector space. It is defined as: $(x * y)_{i} := c l o ((x_{i}^{y_{i}})_{i})_{i}$ The division operation is just the multiplication with $1 / y$ .

References

Aitchison, J. (1986) The Statistical Analysis of Compositional Data Monographs on Statistics and Applied Probability. Chapman & Hall Ltd., London (UK). 416p.

Aitchison, J, C. Barcel'o-Vidal, J.J. Egozcue, V. Pawlowsky-Glahn (2002) A consise guide to the algebraic geometric structure of the simplex, the sample space for compositional data analysis, Terra Nostra, Schriften der Alfred Wegener-Stiftung, 03/2003

Pawlowsky-Glahn, V. and J.J. Egozcue (2001) Geometric approach to statistical analysis on the simplex. SERRA 15(5), 384-398

https://ima.udg.edu/Activitats/CoDaWork03/

https://ima.udg.edu/Activitats/CoDaWork05/

Examples

Run this code

acomp(1:5)* -1 + acomp(1:5)
data(SimulatedAmounts)
cdata <- acomp(sa.lognormals)
plot( tmp <- (cdata-mean(cdata))/msd(cdata) )
class(tmp)
mean(tmp)
msd(tmp)
var(tmp)

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