Calculate quantiles of a numeric vector with associated weights, using the
weighted generalization of the default definition in stats::quantile().
Arguments
- values
Numeric vector of values to compute quantiles for.
- quantiles
Numeric vector of probabilities with values between 0 and 1.
- .weights
Numeric vector of non-negative weights, same length as
values.- na.rm
Logical. If
FALSE(default), a missing value or a missing weight makes every quantile missing. IfTRUE, an observation with either one missing is dropped and the quantiles are computed from the rest.
Value
Numeric vector of weighted quantiles corresponding to the requested
probabilities. Fewer than two observations with a positive weight leave the
quantiles undefined, and the result is NA_real_, as does na.rm = FALSE
with a missing value or a missing weight.
Details
stats::quantile() with type = 7, its default, places the value of rank
i among n values at probability (i - 1) / (n - 1) and interpolates
linearly between them. weighted_quantile() generalizes those positions:
each distinct value spans the probabilities implied by the total weight of
the observations that take it, shortened at each end by half the average
weight of those observations, and the positions are rescaled so that the
smallest value sits at 0 and the largest at 1.
The definition has the properties you would expect of one:
With a constant positive weight, the result is identical to
stats::quantile(values, quantiles), ties included.Multiplying every weight by a constant leaves the result unchanged.
The result does not depend on the order of
values.The result is monotone in
quantiles.
Observations with zero weight contribute nothing and are excluded. This matters for matching weights, which are 0 or 1: the quantiles of a matched sample are the quantiles of the matched observations alone.
Examples
# Equal weights (same as regular quantiles)
weighted_quantile(1:10, c(0.25, 0.5, 0.75), rep(1, 10))
#> [1] 3.25 5.50 7.75
quantile(1:10, c(0.25, 0.5, 0.75))
#> 25% 50% 75%
#> 3.25 5.50 7.75
# Weighted towards higher values
weighted_quantile(1:10, c(0.25, 0.5, 0.75), 1:10)
#> [1] 5.068182 7.100000 8.661765