{ $values { "seq" sequence } { "x" "a non-negative real number"} }
{ $description "Computes the standard deviation of " { $snippet "seq" } ", which is the square root of the variance. It measures how widely spread the values in a sequence are about the mean." }
{ $examples
- { $example "USING: math.statistics prettyprint ;" "{ 4 6 8 10 12 14 16 } std ." "4.0" } } ;
+ { $example "USING: math.statistics prettyprint ;" "{ 7 8 9 } std ." "1.0" } } ;
HELP: ste
{ $values { "seq" sequence } { "x" "a non-negative real number"} }
{ $description "Computes the standard error of the mean for " { $snippet "seq" } ". It's defined as the standard deviation divided by the square root of the length of the sequence, and measures uncertainty associated with the estimate of the mean." }
{ $examples
- { $example "USING: math.statistics prettyprint ;" "{ 4 6 6 8 10 12 14 14 16 } ste ." "1.333333333333333" }
+ { $example "USING: math.statistics prettyprint ;" "{ -2 2 } ste ." "2.0" }
} ;
HELP: var
{ $notes "If the number of elements in " { $snippet "seq" } " is 1 or less, it outputs 0." }
{ $examples
{ $example "USING: math.statistics prettyprint ;" "{ 1 } var ." "0" }
- { $example "USING: math.statistics prettyprint ;" "{ 1 2 3 } var ." "2/3" }
- { $example "USING: math.statistics prettyprint ;" "{ 1 2 3 4 5 } var ." "2" } } ;
+ { $example "USING: math.statistics prettyprint ;" "{ 1 2 3 } var ." "1" }
+ { $example "USING: math.statistics prettyprint ;" "{ 1 2 3 4 } var ." "1+2/3" } } ;
HELP: cov
{ $values { "{x}" sequence } { "{y}" sequence } { "cov" "a real number" } }
{ $subsection "histogram" } ;
ABOUT: "math.statistics"
+
+{ var full-var sample-var } related-words
+{ std full-std sample-std } related-words
+{ ste full-ste sample-ste } related-words
+{ corr full-corr sample-corr } related-words
[ 2 ] [ { 1 2 } upper-median ] unit-test
[ 3/2 ] [ { 1 2 } median ] unit-test
-[ 1 ] [ { 1 2 3 } sample-var ] unit-test
-[ 16 ] [ { 4 6 8 10 10 12 14 16 } sample-var ] unit-test
+[ 1 ] [ { 1 2 3 } var ] unit-test
+[ 16 ] [ { 4 6 8 10 10 12 14 16 } var ] unit-test
-[ 16 ] [ { 4 6 8 10 12 14 16 } var ] unit-test
-[ 4.0 ] [ { 4 6 8 10 12 14 16 } std ] unit-test
+[ 16 ] [ { 4 6 8 10 12 14 16 } full-var ] unit-test
+[ 1.0 ] [ { 7 8 9 } std ] unit-test
[ t ] [ { 1 2 3 4 } ste 0.6454972243679028 - .0001 < ] unit-test
[ t ] [ { 23.2 33.4 22.5 66.3 44.5 } std 18.1906 - .0001 < ] unit-test
[ 0 ] [ { 1 } { 1 } cov ] unit-test
[ 2/3 ] [ { 1 2 3 } { 4 5 6 } cov ] unit-test
-[ 1.0 ] [ { 1 2 3 } { 1 2 3 } corr ] unit-test
-[ -1.0 ] [ { 1 2 3 } { -4 -5 -6 } corr ] unit-test
+[ 0.75 ] [ { 1 2 3 4 } dup corr ] unit-test
+[ -0.75 ] [ { 1 2 3 4 } { -4 -5 -6 -7 } corr ] unit-test
[ { 1 2 4 7 } ] [ { 1 1 2 3 } cum-sum ] unit-test
[ { 1 1 2 6 } ] [ { 1 1 2 3 } cum-product ] unit-test
[ length 1 - ] bi /
] if ;
-: var ( seq -- x )
+: full-var ( seq -- x )
dup length 1 <= [
drop 0
] [
[ length ] bi /
] if ;
-: std ( seq -- x ) var sqrt ;
+ALIAS: var sample-var
-: ste ( seq -- x ) [ std ] [ length ] bi sqrt / ;
+: sample-std ( seq -- x ) sample-var sqrt ;
+
+: full-std ( seq -- x ) full-var sqrt ;
+
+ALIAS: std sample-std
+
+: sample-ste ( seq -- x ) [ sample-std ] [ length ] bi sqrt / ;
+
+: full-ste ( seq -- x ) [ full-std ] [ length ] bi sqrt / ;
+
+ALIAS: ste sample-ste
: ((r)) ( mean(x) mean(y) {x} {y} -- (r) )
! finds sigma((xi-mean(x))(yi-mean(y))
: cov ( {x} {y} -- cov )
[ dup mean v-n ] bi@ v* mean ;
-: corr ( {x} {y} -- corr )
- [ cov ] [ [ var ] bi@ * sqrt ] 2bi / ;
+: sample-corr ( {x} {y} -- corr )
+ [ cov ] [ [ sample-var ] bi@ * sqrt ] 2bi / ;
+
+: full-corr ( {x} {y} -- corr )
+ [ cov ] [ [ full-var ] bi@ * sqrt ] 2bi / ;
+
+ALIAS: corr sample-corr
: cum-sum ( seq -- seq' )
0 swap [ + dup ] map nip ;