Description Usage Arguments Details Value Note Author(s) References See Also Examples

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.

1 2 3 4 5 | ```
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

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

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

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