Transmute weights to turn a generalized mean of order \(r\) into a generalized mean of order \(s\). Useful for calculating additive and multiplicative decompositions for a generalized-mean index, and those made of nested generalized means (e.g., Fisher index).
Arguments
- r, s
A finite number giving the order of the generalized mean. See details.
- r1
A finite number giving the order of the outer generalized mean.
- r2
A pair of finite numbers giving the order of the inner generalized means.
- t
A pair of strictly positive weights for the inner generalized means. The default is equal weights.
Value
transmute_weights() returns a function:
function(x, w = NULL, tol = .Machine$double.eps^0.5){...}nested_transmute() and nested_transmute2() similarly return a
function:
function(x, w1 = NULL, w2 = NULL,
tol = .Machine$double.eps^0.5){...}Details
The function transmute_weights(r, s) returns a function to compute a
vector of weights v(x, w) such that
generalized_mean(r)(x, w) == generalized_mean(s)(x, v(x, w))nested_transmute(r1, r2, t, s) and nested_transmute2(r1, r2, t, s) do
the same for nested generalized means, so that
nested_mean(r1, r2, t)(x, w1, w2) ==
generalized_mean(s)(x, v(x, w1, w2))Transmuting weights returns a value that is the same length as x,
so any missing values in x or the weights will return NA.
Unless all values are NA, however, the result will still satisfy
the above identities when na.rm = TRUE.
References
See vignette("decomposing-indexes") for more details.
See also
generalized_mean() for the generalized mean and nested_mean() for the
nested mean.
extended_mean() for the extended mean that underlies
transmute_weights().
contributions() for calculating additive percent-change
contributions.
grouped() to make these functions operate on grouped data.
Other weights functions:
factor_weights(),
scale_weights()
Examples
x <- 1:3
w <- 3:1
# Calculate the geometric mean as an arithmetic mean and
# harmonic mean by transmuting the weights.
geometric_mean(x)
#> [1] 1.817121
arithmetic_mean(x, transmute_weights(0, 1)(x))
#> [1] 1.817121
harmonic_mean(x, transmute_weights(0, -1)(x))
#> [1] 1.817121
# Works for nested means, too.
w1 <- 3:1
w2 <- 1:3
fisher_mean(x, w1, w2)
#> [1] 1.825742
arithmetic_mean(x, nested_transmute(0, c(1, -1), 1)(x, w1, w2))
#> [1] 1.825742
arithmetic_mean(x, nested_transmute2(0, c(1, -1), 1)(x, w1, w2))
#> [1] 1.825742