factor/extra/math/statistics/statistics.factor

70 lines
1.8 KiB
Factor

USING: kernel math math.analysis math.functions math.vectors sequences
sequences.lib sorting ;
IN: math.statistics
: mean ( seq -- n )
#! arithmetic mean, sum divided by length
[ sum ] keep length / ;
: geometric-mean ( seq -- n )
#! geometric mean, nth root of product
[ product ] keep length swap nth-root ;
: harmonic-mean ( seq -- n )
#! harmonic mean, reciprocal of sum of reciprocals.
#! positive reals only
0 [ recip + ] reduce recip ;
: median ( seq -- n )
#! middle number if odd, avg of two middle numbers if even
natural-sort dup length dup even? [
1- 2 / swap [ nth ] 2keep >r 1+ r> nth + 2 /
] [
2 / swap nth
] if ;
: range ( seq -- n )
#! max - min
minmax swap - ;
: var ( seq -- x )
#! variance, normalize by N-1
dup length 1 <= [
drop 0
] [
[ [ mean ] keep [ - sq ] with sigma ] keep
length 1- /
] if ;
: std ( seq -- x )
#! standard deviation, sqrt of variance
var sqrt ;
: ste ( seq -- x )
#! standard error, standard deviation / sqrt ( length of sequence )
dup std swap length sqrt / ;
: ((r)) ( mean(x) mean(y) {x} {y} -- (r) )
! finds sigma((xi-mean(x))(yi-mean(y))
0 [ [ >r pick r> swap - ] bi@ * + ] 2reduce 2nip ;
: (r) ( mean(x) mean(y) {x} {y} sx sy -- r )
* recip >r [ ((r)) ] keep length 1- / r> * ;
: [r] ( {{x,y}...} -- mean(x) mean(y) {x} {y} sx sy )
first2 [ [ [ mean ] bi@ ] 2keep ] 2keep [ std ] bi@ ;
: r ( {{x,y}...} -- r )
[r] (r) ;
: r^2 ( {{x,y}...} -- r )
r sq ;
: least-squares ( {{x,y}...} -- alpha beta )
[r] >r >r >r >r 2dup r> r> r> r>
! stack is mean(x) mean(y) mean(x) mean(y) {x} {y} sx sy
[ (r) ] 2keep ! stack is mean(x) mean(y) r sx sy
swap / * ! stack is mean(x) mean(y) beta
[ swapd * - ] keep ;