Roger Hui and I have both studied histograms and you can find my discussion at the following link where the following verbs are defined.
http://code.jsoftware.com/wiki/User:Brian_Schott/Histogram To make a long story shorter, my result differs from yours and Roger's when the sample value of 4 changes to a 5, for example. The session below attempts to show that with the verb histogram2 which uses the verb Idotr in place of the primitive verb I. The very last answer differs from its comparisons and I believe follows common statistical definitions of histogram. histogram =: <: @ (#/.~) @ (i. @#@[ , I.) histogram1=: <: @ (#/.~) @ (i.@>:@#@[ , I.) histogram2=: <: @ (#/.~) @ (i.@>:@#@[ , Idotr) Idotr =: |.@[ (#@[-I.) ] 1 3 3 3 4 7 7 8 8 9 histogram ~ 0 2.5 5 7.5 _ 0 1 4 2 3 1 3 3 3 4 7 7 8 8 9 histogram1 ~ 0 2.5 5 7.5 _ 0 1 4 2 3 0 1 3 3 3 4 7 7 8 8 9 histogram2 ~ 0 2.5 5 7.5 _ 0 1 4 2 3 0 1 3 3 3 5 7 7 8 8 9 histogram ~ 0 2.5 5 7.5 _ 0 1 4 2 3 1 3 3 3 5 7 7 8 8 9 histogram1 ~ 0 2.5 5 7.5 _ 0 1 4 2 3 0 1 3 3 3 5 7 7 8 8 9 histogram2 ~ 0 2.5 5 7.5 _ 0 1 3 3 3 0 -- (B=) <-----my sig Brian Schott ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
