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14. Compositions (Based on Hooks and Forks)
A verb is produced by trains of three or two verbs,
as defined by the following diagrams:
FORK HOOK
g g g g
/ \ / \ / \ / \
f h f h y h x h
| | / \ / \ | |
y y x y x y y y
For example, 5(+*-)3 ↔ (5+3)*(5-3) .
The foregoing definition is from
Section II F of the dictionary.
The following examples concern functions used in statistics:
mean=: +/%# Mean
norm=: ] - +/ % # Centered on mean
sqcm=: 2: ^~ ] - +/ % # Sqr of centred on mean
var =: [: mean 2: ^~ ] - mean=: +/%# Variance
stdv=: 2:%:[:mean 2: ^~ ] - mean=: +/%# Standard Deviation
,.&.>@(];mean;norm;sqcm;var;stdv) y=: 2 3 4 5
+-+---+----+----+----+-------+
|2|3.5|_1.5|2.25|1.25|1.11803|
|3| |_0.5|0.25| | |
|4| | 0.5|0.25| | |
|5| | 1.5|2.25| | |
+-+---+----+----+----+-------+
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