Transmute weights for a generalized mean

Transmute weight to turn a generalized mean of a given order into a generalized mean of any other order. Useful for calculating additive and multiplicative decompositions for generalized-mean indexes. See vignette("decomposing-indexes") for more details.

Usage

transmute_weights(x, weights = NULL, order = 0, to = 1, mean = NA)

Arguments

x

[numeric > 0] A strictly positive numeric vector.

weights

[numeric >= 0] A positive numeric vector of weights, the same length as x. The default is to equally weight each element of x.

order

[numeric(1)] A finite number giving the order of the generalized mean. The default transmutes the weights for a geometric mean.

to

[numeric(1)] A finite number giving the order of the target generalized mean. The default computes weights for an arithmetic mean.

mean

[numeric(1)] A finite number giving the generalized mean of x and weights, if known. The default computes this values.

Value

A numeric vector, the same length as x, that sums to 1.

Details

This function generalizes the additive and multiplicative decompositions for arithmetic and geometric indexes by Balk (2008, Chapter 4). It returns a value such that

gmean(x, w, r) == gmean(x, transmute_weights(x, w, r, s), s)

Transmuting weights returns a value that is the same length as x, so any missing values in x or weights will return NA. Unless all values are NA, however, the result will still satisfy the above identity when na.rm = TRUE.

References

Balk, B. M. (2008). Price and Quantity Index Numbers. Cambridge University Press.

See also

Other math functions: emean(), gmean(), nested_gmean(), scale_weights(), transmute_weights2(), update_weights()

Examples

x <- 1:3
w <- 3:1

# Calculate the geometric mean as an arithmetic mean.
gmean(x, order = 0)
#> [1] 1.817121
gmean(x, transmute_weights(x, order = 0, to = 1), order = 1)
#> [1] 1.817121