I'm not completely clear on the requirements, but will this do?
ws =: {. [: (\: ? @: (+ +/) )&:;/ |:
The dyadic verb ws is "weighted selection", where x is the number of items
to select (neccesarily <:#y ) and y is a 2 column table. The first column
gives the universe of elements from which to select, the last column is gives
the weights.
I'm not a statistician, so in the vernacular: for row i and row j of y,
element >(<i;0){y is %/;(<(i,j);1){y times as likely to appear as element
>(<j;0){y . If the universe of elements is numeric, y can be open.
Otherwise it must be boxed (obviously).
Demonstration of use:
universe =. 'ABCDEFG'
weights =. 5 2 3 1 1 1 1
y =. universe ,.&:(<">) weights
3 ws y
ACB
5 ws y
AFDBG
I can neither define nor define the correctness of ws , but this looks pretty
good:
stat_test =. (10000 # 1) ws"0 _ y
counts =. _1 + #/.~ universe , ,stat_test
1 round (% <./) counts % # stat_test [require 'numeric'
5 2 3 1 1 1 1
I hope this helps.
-Dan
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