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Documented correlation and covariance

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Neil Toronto 2012-12-08 22:36:11 -07:00
parent 73395eed94
commit af8d02146d
1 changed files with 48 additions and 1 deletions
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49
collects/math/scribblings/math-statistics.scrbl
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@ -5,6 +5,7 @@
(for-label racket/base racket/promise racket/list
math plot
(only-in typed/racket/base
ann
Flonum Real Boolean Any Listof Integer case-> -> U
Sequenceof Positive-Flonum Nonnegative-Flonum
HashTable Positive-Integer Nonnegative-Real Values))
@ -81,7 +82,7 @@ If some are greater than the largest bound, they are grouped into a single bin a
(bin-samples '(0 1 2 3 4 5 6) '(3) <=)
(bin-samples '(0 1 2 3 4 5 6) '(2 4) <=)]
Note that @racket[bin-samples] always returns bins with @racket[#f] weights, or bins containing
Note that @racket[bin-samples] always returns bins with @racket[#f] weights, meaning they contain
unweighted samples.
}
@ -276,6 +277,52 @@ See @secref{stats:expected-values} for the meaning of the @racket[bias] keyword
@section{Correlation}
@deftogether[(@defproc[(covariance [xs (Sequenceof Real)]
[ys (Sequenceof Real)]
[ws (U #f (Sequenceof Real)) #f]
[#:bias bias (U #t #f Real) #f])
Real]
@defproc[(correlation [xs (Sequenceof Real)]
[ys (Sequenceof Real)]
[ws (U #f (Sequenceof Real)) #f]
[#:bias bias (U #t #f Real) #f])
Real])]{
Compute the sample covariance and correlation of @racket[xs] and @racket[ys], optionally
weighted by @racket[ws].
@examples[#:eval typed-eval
(define xs (sample (normal-dist) 10000))
(define ys (map (λ: ([x : Real]) (sample (normal-dist x))) xs))
(correlation xs ys)]
Removing the correlation using importance weights:
@interaction[#:eval typed-eval
(define ws (map (λ: ([x : Real] [y : Real])
(/ (pdf (normal-dist) y)
(pdf (normal-dist x) y)))
xs ys))
(correlation xs ys (ann ws (Sequenceof Real)))]
See @secref{stats:expected-values} for the meaning of the @racket[bias] keyword argument.
}
@deftogether[(@defproc[(covariance/means [μx Real]
[μy Real]
[xs (Sequenceof Real)]
[ys (Sequenceof Real)]
[ws (U #f (Sequenceof Real)) #f]
[#:bias bias (U #t #f Real) #f])
Real]
@defproc[(correlation/means [μx Real]
[μy Real]
[xs (Sequenceof Real)]
[ys (Sequenceof Real)]
[ws (U #f (Sequenceof Real)) #f]
[#:bias bias (U #t #f Real) #f])
Real])]{
Like @racket[covariance] and @racket[correlation], but computed using known means
@racket[μx] and @racket[μy].
}
@section{Order Statistics}
@(close-eval typed-eval)