Weighted quantiles

Calculates weighted quantiles for a vector of values using linear interpolation between midpoint plotting positions.

Usage

weighted_quantiles(x, w, probs)

Arguments

x

Numeric vector of values

w

Numeric vector of weights (same length as x)

probs

Numeric vector of quantile probabilities (between 0 and 1)

Value

Vector of weighted quantiles

Details

Drops non-finite values and non-positive weights, sorts the survivors by value, then delegates to weighted_quantiles_presorted for the interpolation. (Splitting out the sorted core lets hot callers sort once and reuse the order.)

Each observation is placed at the midpoint of its own weight block, \((\sum_{k \le i} w_k - w_i/2) / \sum_k w_k\), and quantiles are linearly interpolated between those positions. For equal weights the positions are \((i - 0.5)/n\), so the unweighted case reduces to the standard Hazen (type-5) quantile. Before v0.71.1 the upper edge \(\sum_{k \le i} w_k\) was used instead, which biased every quantile downward in proportion to how concentrated the weights were; see NEWS for the size of the effect on calc_model_ensemble().

Examples

x <- c(1, 2, 3, 4, 5)
w <- c(0.1, 0.2, 0.4, 0.2, 0.1)
weighted_quantiles(x, w, c(0.25, 0.5, 0.75))
#> [1] 2.166667 3.000000 3.833333