Calculation of median/quantiles

[akdixon]

I'm trying to calculate the median value of the pixels within a polygon using exact_extract, but it's giving me weird values. Here's some example code.

rast <- raster::raster(matrix(c(0,0,0,0,10,0,0,0,0), ncol=3),xmn=0, ymn=0, xmx=3, ymx=3)
poly <- sf::st_as_sfc('POLYGON ((1 1, 1 3, 3 3, 3 1, 1 1))')
exact_extract(rast, poly, "median")
exact_extract(rast, poly, "quantile", quantiles = 0.5)
exact_extract(rast, poly, "mean")

The mean seems correct with an output of 2.5, but for "median" it's producing 5. Shouldn't it be 0 if the values used are 0, 0, 0, 10? Am I misunderstanding something about how the median/quantiles are calculated? I'm not great at coding and definitely could have missed something in the documentation, so sorry if this is answered somewhere else. Thanks!

[dbaston]

The formula being used is this one: https://stats.stackexchange.com/a/13223

Why this formula? From my notes of several years ago:

// Unlike spatstat::weighted.quantile, it matches the default behavior of the
// base R stats::quantile function when all weights are equal.
// Unlike Hmisc::wtd.quantile, quantiles always change as the probability is
// changed, unless there are duplicate values.

Equal-value pixels are being combined (and their weights added) before being passed to this function, so rather than equally-weighted values of (0, 0, 0, 10) we have values of 0 and 10 with weights of 3 and 1.

I notice that spatstat.univar::weighted.quantile(c(0,10), c(3, 1), 0.5) gives the expected result of zero.

[dbaston]

See also https://search.r-project.org/CRAN/refmans/spatstat.univar/html/weighted.median.html