factor_weights: Factor weights

In gpindex: Generalized Price and Quantity Indexes

Factor weights

Description

Factor weights to turn the generalized mean of a product into the product of generalized means. Useful for price-updating the weights in a generalized-mean index.

Usage

factor_weights(r)

update_weights(x, w = NULL)

Arguments

r	A finite number giving the order of the generalized mean.
x	A strictly positive numeric vector.
w	A strictly positive numeric vector of weights, the same length as x. The default is to equally weight each element of x.

Details

The function factor_weights(r) returns a function to compute weights u(x, w) such that

generalized_mean(r)(x * y, w) ==
  generalized_mean(r)(x, w) * generalized_mean(r)(y, u(x, w))

This generalizes the result in section C.5 of Chapter 9 of the PPI Manual for chaining the Young index, and gives a way to chain generalized-mean price indexes over time.

Factoring weights with r = 1 sometimes gets called price-updating weights; update_weights() simply calls factor_weights(1)().

Factoring weights return 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 for will still satisfy the above identity when na.rm = TRUE.

Value

factor_weights() return a function:

function(x, w = NULL){...}

update_weights() returns a numeric vector the same length as x.

References

ILO, IMF, OECD, Eurostat, UN, and World Bank. (2004). Producer Price Index Manual: Theory and Practice. International Monetary Fund.

See Also

generalized_mean() for the generalized mean.

grouped() to make these functions operate on grouped data.

Other weights: scale_weights(), transmute_weights()

Examples

x <- 1:3
y <- 4:6
w <- 3:1
# Factor the harmonic mean by chaining the calculation

harmonic_mean(x * y, w)
harmonic_mean(x, w) * harmonic_mean(y, factor_weights(-1)(x, w))

# The common case of an arithmetic mean

arithmetic_mean(x * y, w)
arithmetic_mean(x, w) * arithmetic_mean(y, update_weights(x, w))

# In cases where x and y have the same order, Chebyshev's
# inequality implies that the chained calculation is too small

arithmetic_mean(x * y, w) >
  arithmetic_mean(x, w) * arithmetic_mean(y, w)

gpindex documentation built on Nov. 15, 2023, 9:06 a.m.