acomparith | R Documentation |
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.
power.acomp(x,s)
## Methods for class "acomp"
## x*y
## x/y
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) |
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
.
An "acomp"
vector or matrix.
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.
K.Gerald v.d. Boogaart http://www.stat.boogaart.de
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/
ilr
,clr
, alr
,
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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