The dyad I. and the monad #/.~ can be used to compute histograms efficiently:
histogram=: <: @ (#/.~) @ (i.@#@[ , I.)
The left argument is a list of interval start points. The right argument is an array of data. The result is a list of counts of the number of data points in each interval.
The following example illustrates the central limit theorem: the sum of independent identically distributed random variables converges in distribution to a normal random variable.
d=: +/ 10 1e6 ?.@$ 21 e=: 5 * i.40 h=: e histogram d $ h 40 h 0 0 0 0 1 6 38 151 400 1093 2417 5274 9732 17014 26482 39266 54622 70277 85594 96077 101359 101033 94374 82241 67322 52201 36777 24419 15174 8526 4666 2091 880 348 99 34 12 0 0 0 load 'plot' plot e;h
Contributed by RogerHui.