gpindex (version 0.6.3)

transmute_weights: Transmute weights

Description

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).

Usage

transmute_weights(r, s)
nested_transmute(r1, r2, s, t = c(1, 1))
nested_transmute2(r1, r2, s, t = c(1, 1))

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){...}

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.

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)
arithmetic_mean(x, transmute_weights(0, 1)(x))
harmonic_mean(x, transmute_weights(0, -1)(x))

# Works for nested means, too.

w1 <- 3:1
w2 <- 1:3

fisher_mean(x, w1, w2)

arithmetic_mean(x, nested_transmute(0, c(1, -1), 1)(x, w1, w2))
arithmetic_mean(x, nested_transmute2(0, c(1, -1), 1)(x, w1, w2))