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2002 Feb 06
4
Weighted median
Is there a weighted median function out there similar to weighted.mean()
but for medians? If not, I'll try implement or port it myself.
The need for a weighted median came from the following optimization
problem:
x* = arg_x min (a|x| + sum_{k=1}^n |x - b_k|)
where
a : is a *positive* real scalar
x : is a real scalar
n : is an integer
b_k: are negative and positive scalars
which is a "median with a shift towards zero". This can be rewritten as
x* = arg_x min (sum_{k=0}^n w_k|x - b_k|)
where...