piar (version 0.10.1)

transmute_weights: Transmute weights for a generalized mean

Description

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)

Value

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

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.

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)
gmean(x, transmute_weights(x, order = 0, to = 1), order = 1)