769e8b47ec
Cleaned up expected value code a little Refactored running statistics objects (hid private fields, added `update-statistics*') Documented expected value functions and running statistics Removed `bfpsi0' from bigfloat tests (DrDr's libmpfr doesn't have it) Commented out custodian shutdown callback that frees MPFR's cache (something's broken)
132 lines
6.1 KiB
Racket
132 lines
6.1 KiB
Racket
#lang typed/racket/base
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(require racket/sequence
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"../../base.rkt"
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"statistics-utils.rkt")
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(provide mean
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variance/mean
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stddev/mean
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skewness/mean
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kurtosis/mean
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variance
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stddev
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skewness
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kurtosis)
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(: mean (case-> ((Sequenceof Real) -> Real)
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((Sequenceof Real) (Option (Sequenceof Real)) -> Real)))
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(define (mean xs [ws #f])
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(cond [ws (let-values ([(xs ws) (sequences->weighted-samples 'mean xs ws)])
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(define n (sum ws))
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(cond [(zero? n) +nan.0]
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[else (/ (sum (map * xs ws)) n)]))]
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[else (let ([xs (sequence->list xs)])
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(define n (length xs))
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(cond [(zero? n) +nan.0]
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[else (/ (sum xs) n)]))]))
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(: variance* (Symbol Real (Sequenceof Real) (Option (Sequenceof Real)) (U #t #f Real)
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-> Nonnegative-Real))
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(define (variance* name m xs ws bias)
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(define-values (xs^2 n)
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(cond [ws (let-values ([(xs ws) (sequences->weighted-samples name xs ws)])
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(values (map (λ: ([x : Real] [w : Real]) (* w (sqr (- x m)))) xs ws)
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(max 0 (sum ws))))]
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[else (let ([xs (sequence->list xs)])
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(values (map (λ: ([x : Real]) (sqr (- x m))) xs)
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(length xs)))]))
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(cond [(zero? n) +nan.0]
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[else
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(define m2 (max 0 (/ (sum xs^2) n)))
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(adjust-variance m2 n bias)]))
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(: skewness* (Symbol Real (Sequenceof Real) (Option (Sequenceof Real)) (U #t #f Real) -> Real))
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(define (skewness* name m xs ws bias)
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(define-values (xs^2 xs^3 n)
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(cond [ws (let-values ([(xs ws) (sequences->weighted-samples name xs ws)])
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(values (map (λ: ([x : Real] [w : Real]) (* w (sqr (- x m)))) xs ws)
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(map (λ: ([x : Real] [w : Real]) (* w (expt (- x m) 3))) xs ws)
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(max 0 (sum ws))))]
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[else (let ([xs (sequence->list xs)])
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(values (map (λ: ([x : Real]) (sqr (- x m))) xs)
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(map (λ: ([x : Real]) (expt (- x m) 3)) xs)
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(length xs)))]))
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(cond [(zero? n) +nan.0]
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[else
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(define m2 (expt (max 0 (sum xs^2)) 3/2))
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(cond [(zero? m2) +nan.0]
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[else
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(define m3 (sum xs^3))
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(adjust-skewness (/ (* m3 (sqrt n)) m2) n bias)])]))
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(: kurtosis* (Symbol Real (Sequenceof Real) (Option (Sequenceof Real)) (U #t #f Real)
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-> Nonnegative-Real))
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(define (kurtosis* name m xs ws bias)
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(define-values (xs^2 xs^4 n)
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(cond [ws (let-values ([(xs ws) (sequences->weighted-samples name xs ws)])
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(values (map (λ: ([x : Real] [w : Real]) (* w (sqr (- x m)))) xs ws)
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(map (λ: ([x : Real] [w : Real]) (* w (expt (- x m) 4))) xs ws)
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(max 0 (sum ws))))]
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[else (let ([xs (sequence->list xs)])
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(values (map (λ: ([x : Real]) (sqr (- x m))) xs)
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(map (λ: ([x : Real]) (expt (- x m) 4)) xs)
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(length xs)))]))
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(cond [(zero? n) +nan.0]
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[else
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(define m2 (sum xs^2))
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(cond [(zero? m2) +nan.0]
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[else
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(define m4 (sum xs^4))
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(adjust-kurtosis (max 0 (/ (* (/ m4 m2) n) m2)) n bias)])]))
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;; ===================================================================================================
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;; User-facing functions
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(: variance/mean (case-> (Real (Sequenceof Real) [#:bias (U #t #f Real)] -> Nonnegative-Real)
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(Real (Sequenceof Real) (Option (Sequenceof Real)) [#:bias (U #t #f Real)]
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-> Nonnegative-Real)))
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(define (variance/mean m xs [ws #f] #:bias [bias #f])
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(variance* 'variance/mean m xs ws bias))
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(: variance (case-> ((Sequenceof Real) [#:bias (U #t #f Real)] -> Nonnegative-Real)
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((Sequenceof Real) (Option (Sequenceof Real)) [#:bias (U #t #f Real)]
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-> Nonnegative-Real)))
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(define (variance xs [ws #f] #:bias [bias #f])
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(variance* 'variance (mean xs ws) xs ws bias))
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(: stddev/mean (case-> (Real (Sequenceof Real) [#:bias (U #t #f Real)] -> Nonnegative-Real)
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(Real (Sequenceof Real) (Option (Sequenceof Real)) [#:bias (U #t #f Real)]
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-> Nonnegative-Real)))
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(define (stddev/mean m xs [ws #f] #:bias [bias #f])
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(sqrt (variance* 'stddev/mean (mean xs ws) xs ws bias)))
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(: stddev (case-> ((Sequenceof Real) [#:bias (U #t #f Real)] -> Nonnegative-Real)
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((Sequenceof Real) (Option (Sequenceof Real)) [#:bias (U #t #f Real)]
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-> Nonnegative-Real)))
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(define (stddev xs [ws #f] #:bias [bias #f])
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(sqrt (variance* 'stddev (mean xs ws) xs ws bias)))
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(: skewness/mean (case-> (Real (Sequenceof Real) [#:bias (U #t #f Real)] -> Real)
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(Real (Sequenceof Real) (Option (Sequenceof Real)) [#:bias (U #t #f Real)]
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-> Real)))
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(define (skewness/mean m xs [ws #f] #:bias [bias #f])
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(skewness* 'skewness/mean m xs ws bias))
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(: skewness (case-> ((Sequenceof Real) [#:bias (U #t #f Real)] -> Real)
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((Sequenceof Real) (Option (Sequenceof Real)) [#:bias (U #t #f Real)] -> Real)))
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(define (skewness xs [ws #f] #:bias [bias #f])
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(skewness* 'skewness (mean xs ws) xs ws bias))
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(: kurtosis/mean (case-> (Real (Sequenceof Real) [#:bias (U #t #f Real)] -> Nonnegative-Real)
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(Real (Sequenceof Real) (Option (Sequenceof Real)) [#:bias (U #t #f Real)]
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-> Nonnegative-Real)))
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(define (kurtosis/mean m xs [ws #f] #:bias [bias #f])
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(kurtosis* 'kurtosis/mean m xs ws bias))
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(: kurtosis (case-> ((Sequenceof Real) [#:bias (U #t #f Real)] -> Nonnegative-Real)
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((Sequenceof Real) (Option (Sequenceof Real)) [#:bias (U #t #f Real)]
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-> Nonnegative-Real)))
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(define (kurtosis xs [ws #f] #:bias [bias #f])
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(kurtosis* 'kurtosis (mean xs ws) xs ws bias))
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