Mean of a compositional sample taken in log-ratio coordinates

Formula: mean clr = (1/n) sum_k clr(x_k); centre = clr^-1(mean clr)

Usage

Complrm(X, total = 1)

Arguments

X

One composition per row; strictly positive.

total

Constant the returned centre sums to.

Value

List with clr_mean, center, sum_clr_mean, n, D.

References

Aitchison (1986), The Statistical Analysis of Compositional Data, Chapter 4. Consistent with the sibling module aitcen in this package, whose centre is the closed vector of column geometric means.

Examples

V <- c(1, 2, 3, 4, 5, 6, 7, 8)
Complrm(V)
#> $clr_mean
#> [1] 0
#> 
#> $center
#> [1] 1
#> 
#> $sum_clr_mean
#> [1] 0
#> 
#> $n
#> [1] 8
#> 
#> $D
#> [1] 1
#> 
#> $method
#> [1] "Log-ratio mean (clr average, closed back)"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"