stacked_quantile

'Stacked' quantile functions. Close to weighted quantile functions.

These functions are used to calculate quantiles of a set of values, where each value has a weight. The typical process for calculating a weighted quantile is to create a CDF from the weights, then interpolate the values to find the quantile.

These functions, however, treat weighted values (given integer weights) exactly as multiple values.

So, values (1, 2, 3) with weights (4, 5, 6) will be treated as

(1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3)

If the quantile falls exactly between two values, the non-weighted average of the two values is returned. This is consistent with the "weights as occurrences" interpretation. Strips all zero-weight values, so these will never be included in such averages.

If using non-integer weights, the results will be as if some scalar were applied to make all weights into integers.

This "weights as occurrences" interpretation has two pitfalls:

1. Identical values will be returned for different quantiles (e.g., the results for quantiles == 0.5, 0.6, and 0.7 might be identical). The effect of this is that some some common data practices like "robust scalar" will not be robust because of the potential for a 0 interquartile range. Again this is consistent, because the same thing could happen with repeated, non-weighted values.

2. With any number of values, the stacked_median could still be the first or last value (if it has enough weight), so separating by the median is not robust. This could also happen with repeaded, non-weighted values. One workaround is to divide the values into group_a = values strictly < median, group_b = values strictly > median, then add == median to the smaller group.