acomparith {compositions}R Documentation

Power transform in Aitchisons 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
          

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)

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:= clo( (x_i^{y_i})_i )_i

The division operation is just the multiplication with 1/y.

Value

An "acomp" vector or matrix.

Note

For * the arguments x and y can be exchanged. Note that this definition generalizes the power by a scalar, since y or s may be given as a scalar, or as a vector with as many components as the composition in acomp x. The result is then a matrix where each row corresponds to the composition powered by one of the scalars in the vector.

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

http://ima.udg.es/Activitats/CoDaWork03

http://ima.udg.es/Activitats/CoDaWork05

See Also

ilr,clr, alr,

Examples

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)

[Package compositions version 0.9-10 Index]