math.statistics: Make you think about which std you want--population or sample. Hopefully use the right words everywhere.
Doug Coleman
parent
d291f096c2
commit
c20ee965c6
|
|
@ -46,33 +46,33 @@ HELP: minmax
|
|||
}
|
||||
} ;
|
||||
|
||||
HELP: std
|
||||
HELP: sample-std
|
||||
{ $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." }
|
||||
{ $description "Computes the sample standard deviation of " { $snippet "seq" } ", which is the square root of the sample variance. It measures how widely spread the values in a sequence are about the mean for a random subset of a dataset." }
|
||||
{ $examples
|
||||
{ $example "USING: math.statistics prettyprint ;" "{ 7 8 9 } std ." "1.0" } } ;
|
||||
{ $example "USING: math.statistics prettyprint ;" "{ 7 8 9 } sample-std ." "1.0" } } ;
|
||||
|
||||
HELP: ste
|
||||
HELP: sample-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 ;" "{ -2 2 } ste ." "2.0" }
|
||||
{ $example "USING: math.statistics prettyprint ;" "{ -2 2 } sample-ste ." "2.0" }
|
||||
} ;
|
||||
|
||||
HELP: var
|
||||
HELP: sample-var
|
||||
{ $values { "seq" sequence } { "x" "a non-negative real number"} }
|
||||
{ $description "Computes the variance of " { $snippet "seq" } ". It's a measurement of the spread of values in a sequence. The larger the variance, the larger the distance of values from the mean." }
|
||||
{ $description "Computes the variance of " { $snippet "seq" } ". It's a measurement of the spread of values in a sequence." }
|
||||
{ $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 ." "1" }
|
||||
{ $example "USING: math.statistics prettyprint ;" "{ 1 2 3 4 } var ." "1+2/3" } } ;
|
||||
{ $example "USING: math.statistics prettyprint ;" "{ 1 } sample-var ." "0" }
|
||||
{ $example "USING: math.statistics prettyprint ;" "{ 1 2 3 } sample-var ." "1" }
|
||||
{ $example "USING: math.statistics prettyprint ;" "{ 1 2 3 4 } sample-var ." "1+2/3" } } ;
|
||||
|
||||
HELP: cov
|
||||
HELP: population-cov
|
||||
{ $values { "{x}" sequence } { "{y}" sequence } { "cov" "a real number" } }
|
||||
{ $description "Computes the covariance of two sequences, " { $snippet "{x}" } " and " { $snippet "{y}" } "." } ;
|
||||
|
||||
HELP: corr
|
||||
HELP: population-corr
|
||||
{ $values { "{x}" sequence } { "{y}" sequence } { "corr" "a real number" } }
|
||||
{ $description "Computes the correlation of two sequences, " { $snippet "{x}" } " and " { $snippet "{y}" } "." } ;
|
||||
|
||||
|
|
@ -281,8 +281,12 @@ ARTICLE: "math.statistics" "Statistics"
|
|||
{ $subsections median lower-median upper-median medians }
|
||||
"Computing the mode:"
|
||||
{ $subsections mode }
|
||||
"Computing the standard deviation, standard error, and variance:"
|
||||
{ $subsections std ste var }
|
||||
"Computing the population standard deviation, standard error, and variance:"
|
||||
{ $subsections population-std population-ste population-var }
|
||||
"Computing the sample standard deviation, standard error, and variance:"
|
||||
{ $subsections sample-std sample-ste sample-var }
|
||||
"Computing the nth delta-degrees-of-freedom statistics:"
|
||||
{ $subsections std-ddof ste-ddof var-ddof }
|
||||
"Computing the range and minimum and maximum elements:"
|
||||
{ $subsections range minmax }
|
||||
"Computing the kth smallest element:"
|
||||
|
|
@ -294,7 +298,8 @@ ARTICLE: "math.statistics" "Statistics"
|
|||
|
||||
ABOUT: "math.statistics"
|
||||
|
||||
{ var var-ddof population-var sample-var } related-words
|
||||
{ std std-ddof population-std sample-std } related-words
|
||||
{ ste ste-ddof population-ste sample-ste } related-words
|
||||
{ corr corr-ddof population-corr sample-corr } related-words
|
||||
{ var-ddof population-var sample-var } related-words
|
||||
{ std-ddof population-std sample-std } related-words
|
||||
{ ste-ddof population-ste sample-ste } related-words
|
||||
{ corr-ddof population-corr sample-corr } related-words
|
||||
{ cov-ddof population-cov sample-cov } related-words
|
||||
|
|
|
|||
|
|
@ -52,15 +52,14 @@ IN: math.statistics.tests
|
|||
[ 2 ] [ { 1 2 } upper-median ] unit-test
|
||||
[ 3/2 ] [ { 1 2 } median ] unit-test
|
||||
|
||||
[ 1 ] [ { 1 2 3 } var ] unit-test
|
||||
[ 16 ] [ { 4 6 8 10 10 12 14 16 } var ] unit-test
|
||||
[ 1 ] [ { 1 2 3 } sample-var ] unit-test
|
||||
[ 16 ] [ { 4 6 8 10 10 12 14 16 } sample-var ] unit-test
|
||||
|
||||
{ 16 } [ { 4 6 8 10 12 14 16 } population-var ] unit-test
|
||||
{ 1.0 } [ { 7 8 9 } std ] unit-test
|
||||
{ 1.0 } [ { 7 8 9 } sample-std ] unit-test
|
||||
{ 2/3 } [ { 7 8 9 } 0 var-ddof ] unit-test
|
||||
{ 2/3 } [ { 7 8 9 } population-var ] unit-test
|
||||
{ 1 } [ { 7 8 9 } 1 var-ddof ] unit-test
|
||||
{ 1 } [ { 7 8 9 } var ] unit-test
|
||||
{ 1 } [ { 7 8 9 } sample-var ] unit-test
|
||||
{ 2 } [ { 7 8 9 } 2 var-ddof ] unit-test
|
||||
{ 0 } [ { 7 8 9 } 3 var-ddof ] unit-test
|
||||
|
|
@ -68,18 +67,18 @@ IN: math.statistics.tests
|
|||
{ t } [ { 7 8 9 } 0 std-ddof 0.816496580927726 .0001 ~ ] unit-test
|
||||
{ t } [ { 7 8 9 } population-std 0.816496580927726 .0001 ~ ] unit-test
|
||||
{ 1.0 } [ { 7 8 9 } 1 std-ddof ] unit-test
|
||||
{ 1.0 } [ { 7 8 9 } std ] unit-test
|
||||
{ 1.0 } [ { 7 8 9 } sample-std ] unit-test
|
||||
{ 1.0 } [ { 7 8 9 } sample-std ] unit-test
|
||||
{ t } [ { 7 8 9 } 2 std-ddof 1.414213562373095 .0001 ~ ] unit-test
|
||||
{ 0.0 } [ { 7 8 9 } 3 std-ddof ] unit-test
|
||||
|
||||
[ t ] [ { 1 2 3 4 } ste 0.6454972243679028 - .0001 < ] unit-test
|
||||
[ t ] [ { 1 2 3 4 } sample-ste 0.6454972243679028 - .0001 < ] unit-test
|
||||
|
||||
[ t ] [ { 23.2 33.4 22.5 66.3 44.5 } std 18.1906 - .0001 < ] unit-test
|
||||
[ t ] [ { 23.2 33.4 22.5 66.3 44.5 } sample-std 18.1906 - .0001 < ] unit-test
|
||||
|
||||
[ 0 ] [ { 1 } var ] unit-test
|
||||
[ 0.0 ] [ { 1 } std ] unit-test
|
||||
[ 0.0 ] [ { 1 } ste ] unit-test
|
||||
[ 0 ] [ { 1 } sample-var ] unit-test
|
||||
[ 0.0 ] [ { 1 } sample-std ] unit-test
|
||||
[ 0.0 ] [ { 1 } sample-ste ] unit-test
|
||||
|
||||
{ 2 } [ { 1 3 5 7 } mean-dev ] unit-test
|
||||
{ 4/5 } [ { 1 3 3 3 5 } median-dev ] unit-test
|
||||
|
|
@ -106,11 +105,12 @@ IN: math.statistics.tests
|
|||
[ 0 swap at ] [ 1 swap at ] [ 2 swap at ] tri
|
||||
] unit-test
|
||||
|
||||
[ 0 ] [ { 1 } { 1 } cov ] unit-test
|
||||
[ 2/3 ] [ { 1 2 3 } { 4 5 6 } cov ] unit-test
|
||||
[ 0 ] [ { 1 } { 1 } sample-cov ] unit-test
|
||||
[ 2/3 ] [ { 1 2 3 } { 4 5 6 } population-cov ] 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
|
||||
[ 0.75 ] [ { 1 2 3 4 } dup sample-corr ] unit-test
|
||||
[ 1.0 ] [ { 1 2 3 4 } dup population-corr ] unit-test
|
||||
[ -0.75 ] [ { 1 2 3 4 } { -4 -5 -6 -7 } sample-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
|
||||
|
|
@ -173,7 +173,14 @@ IN: math.statistics.tests
|
|||
|
||||
{ t t } [
|
||||
{ 6.5 3.8 6.6 5.7 6.0 6.4 5.3 } standardize
|
||||
[ mean 0 1e-10 ~ ] [ var 1 1e-10 ~ ] bi
|
||||
[ mean 0 1e-10 ~ ] [ sample-var 1 1e-10 ~ ] bi
|
||||
] unit-test
|
||||
|
||||
{ t t } [
|
||||
{ { 1 -1 2 } { 2 0 0 } { 0 1 -1 } } standardize-2d
|
||||
flip
|
||||
[ [ mean ] map { 0 0 0 } 1e-10 v~ ]
|
||||
[ [ sample-var ] map { 1 1 1 } 1e-10 v~ ] bi
|
||||
] unit-test
|
||||
|
||||
{ { 0 0 0 } } [ { 1 1 1 } standardize ] unit-test
|
||||
|
|
|
|||
|
|
@ -265,8 +265,6 @@ PRIVATE>
|
|||
|
||||
: sample-var ( seq -- x ) 1 var-ddof ; inline
|
||||
|
||||
ALIAS: var sample-var
|
||||
|
||||
: std-ddof ( seq n -- x )
|
||||
var-ddof sqrt ; inline
|
||||
|
||||
|
|
@ -274,9 +272,7 @@ ALIAS: var sample-var
|
|||
|
||||
: sample-std ( seq -- x ) 1 std-ddof ; inline
|
||||
|
||||
ALIAS: std sample-std
|
||||
|
||||
: signal-to-noise ( seq -- x ) [ mean ] [ std ] bi / ;
|
||||
: signal-to-noise ( seq -- x ) [ mean ] [ population-std ] bi / ;
|
||||
|
||||
: mean-dev ( seq -- x ) dup mean v-n vabs mean ;
|
||||
|
||||
|
|
@ -288,8 +284,6 @@ ALIAS: std sample-std
|
|||
|
||||
: sample-ste ( seq -- x ) 1 ste-ddof ;
|
||||
|
||||
ALIAS: ste sample-ste
|
||||
|
||||
: ((r)) ( mean(x) mean(y) {x} {y} -- (r) )
|
||||
! finds sigma((xi-mean(x))(yi-mean(y))
|
||||
0 [ [ [ pick ] dip swap - ] bi@ * + ] 2reduce 2nip ;
|
||||
|
|
@ -298,7 +292,7 @@ ALIAS: ste sample-ste
|
|||
* recip [ [ ((r)) ] keep length 1 - / ] dip * ;
|
||||
|
||||
: [r] ( {{x,y}...} -- mean(x) mean(y) {x} {y} sx sy )
|
||||
first2 [ [ [ mean ] bi@ ] 2keep ] 2keep [ std ] bi@ ;
|
||||
first2 [ [ [ mean ] bi@ ] 2keep ] 2keep [ population-std ] bi@ ;
|
||||
|
||||
: r ( {{x,y}...} -- r )
|
||||
[r] (r) ;
|
||||
|
|
@ -316,20 +310,18 @@ ALIAS: ste sample-ste
|
|||
: cov-ddof ( {x} {y} ddof -- cov )
|
||||
[ [ dup mean v-n ] bi@ v* ] dip mean-ddof ;
|
||||
|
||||
: cov ( {x} {y} -- cov ) 0 cov-ddof ; inline
|
||||
: population-cov ( {x} {y} -- cov ) 0 cov-ddof ; inline
|
||||
|
||||
: unbiased-cov ( {x} {y} -- cov ) 1 cov-ddof ; inline
|
||||
: sample-cov ( {x} {y} -- cov ) 1 cov-ddof ; inline
|
||||
|
||||
: corr-ddof ( {x} {y} n -- corr )
|
||||
[ [ cov ] ] dip
|
||||
[ [ population-cov ] ] dip
|
||||
'[ [ _ var-ddof ] bi@ * sqrt ] 2bi / ;
|
||||
|
||||
: population-corr ( {x} {y} -- corr ) 0 corr-ddof ; inline
|
||||
|
||||
: sample-corr ( {x} {y} -- corr ) 1 corr-ddof ; inline
|
||||
|
||||
ALIAS: corr sample-corr
|
||||
|
||||
: cum-map ( seq identity quot -- seq' )
|
||||
swapd [ dup ] compose map nip ; inline
|
||||
|
||||
|
|
@ -368,11 +360,11 @@ ALIAS: corr sample-corr
|
|||
[ dup log * ] [ 1 swap - dup log * ] bi + neg 2 log / ;
|
||||
|
||||
: standardize ( u -- v )
|
||||
[ dup mean v-n ] [ std ] bi
|
||||
[ dup mean v-n ] [ sample-std ] bi
|
||||
dup zero? [ drop ] [ v/n ] if ;
|
||||
|
||||
: standardize-2d ( u -- v )
|
||||
flip dup [ [ mean ] [ std ] bi 2array ] map
|
||||
flip dup [ [ mean ] [ sample-std ] bi 2array ] map
|
||||
[ [ first v-n ] 2map ] keep [ second v/n ] 2map flip ;
|
||||
|
||||
: differences ( u -- v )
|
||||
|
|
|
|||
Loading…
Reference in New Issue