piar (version 0.10.1)

update_weights: Update 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

update_weights(x, weights = NULL, order = 1)

Value

A numeric vector the same length as x.

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 (or exponent) of the generalized mean. The default calculates an arithmetic mean.

Details

This function 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. It returns a value such that

gmean(x * y, w) ==
    gmean(x, w) * gmean(y, update_weights(x, w))

Factoring 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

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

See Also

Other math functions: emean(), gmean(), nested_gmean(), scale_weights(), transmute_weights(), transmute_weights2()

Examples

x <- 1:3
y <- 4:6
w <- 3:1

# Factor the arithmetic mean by chaining the calculation.
gmean(x * y, w)
gmean(x, w) * gmean(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.
gmean(x * y, w) > gmean(x, w) * gmean(y, w)