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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