KDB: weighted median

For values v and weights w, med v where w gobbles space for larger values of w.

Instead, sort w into ascending order of v and look for where cumulative sums reach half their sum.

q)show v:10?100
17 23 12 66 36 37 44 28 20 30
q)show w:.001*10?1000
0.418 0.126 0.077 0.829 0.503 0.12 0.71 0.506 0.804 0.012
q)med v where "j"$w*1000
36f

q)w iasc v / sort w into ascending order of v
0.077 0.418 0.804 0.126 0.506 0.012 0.503 0.12 0.71 0.829
q)0.5 1*(sum;sums)@\:w iasc v / half the sum and cumulative sums of w
2.0525
0.077 0.495 1.299 1.425 1.931 1.943 2.446 2.566 3.276 4.105
q).[>]0.5 1*(sum;sums)@\:w iasc v / compared
1111110000b
q)v i sum .[>]0.5 1*(sum;sums)@\:w i:iasc v / weighted median
36

q)\ts:1000 med v where "j"$w*1000
18 132192
q)\ts:1000 v i sum .[>]0.5 1*(sum;sums)@\:w i:iasc v
2 2576

q)wmed:{x i sum .[>]0.5 1*(sum;sums)@\:y i:iasc x}

Some vector techniques worth noticing:

• Applying two functions with Each Left (sum;sums)@\: and using Apply . and an operator on the result, rather than setting a variable, e.g. (0.5*sum yi)>sums yi:y i or defining an inner lambda {sums[x]<0.5*sum x}y i
• Grading one list with iasc to sort another
• Multiple mappings through juxtaposition: v i sum ..

You could effectively weight the median by duplicating (using where):

q)med 10 34 23 123 5 56 where 4 1 1 1 1 1
10f
q)med 10 34 23 123 5 56 where 1 1 1 1 1 4
56f
q)med 10 34 23 123 5 56 where 1 2 1 3 2 1
34f

If your weights are percentages (e.g. 0.15 0.10 0.20 0.30 0.25) then convert them to equivalent whole/counting numbers

q)med 1 2 3 4 5 where "i"$100*0.15 0.10 0.20 0.30 0.25
4f