piar (version 0.10.1)

transmute_weights2: Transmute weights for a nested generalized mean

Description

Transmute weights to turn a nested generalized mean of a given order into a generalized mean of any order. Useful for calculating additive and multiplicative decompositions for an index made of nested generalized means (e.g., Fisher index). See vignette("decomposing-indexes") for details.

Usage

transmute_weights2(
  x,
  weights = list(NULL, NULL),
  order = c(1, -1),
  outer_weights = NULL,
  outer_order = 0,
  to = 1,
  pivot = outer_order
)

Value

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

Arguments

x

[numeric > 0] A strictly positive numeric vector.

weights

[list] A list of positive numeric vector of weights, each the same length as x, for both of the inner generalized means. NULL elements of weights equally weight each element of x. The default uses equal weights for both inner generalized mean.

order

[numeric(2)] A finite numeric vector giving the order of each of the inner generalized means. The default computes an arithmetic mean and a harmonic mean.

outer_weights

[numeric(2)] A strictly positive numeric vector weights for each of the inner generalized means as used in the outer generalized mean. The default weights each inner generalized mean equally.

outer_order

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

to

A finite number giving the order of the target generalized mean for the transmuted weights. The default constructs weights for an arithmetic mean.

pivot

A finite number giving the pivot value for the transmuted weights. The default uses the order of the outer generalized mean, otherwise to is common alternative.

Details

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

nested_gmean(x, list(w1, w2), c(r1, r2)) ==
    gmean(x, transmute_weights2(x, list(w1, w2), c(r1, r2), to = 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_weights(), update_weights()

Examples

x <- 1:3
w1 <- 3:1
w2 <- c(1, 2, 1)

# Calculate the geometric mean of the arithmetic and harmonic means
# as an arithmetic mean.
nested_gmean(x, list(w1, w2))
gmean(x, transmute_weights2(x, list(w1, w2), to = 1))