138 lines
2.9 KiB
Go
138 lines
2.9 KiB
Go
// Package onlinestats provides online, one-pass algorithms for descriptive statistics.
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/*
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The implementation is based on the public domain code available at http://www.johndcook.com/skewness_kurtosis.html .
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The linear regression code is from http://www.johndcook.com/running_regression.html .
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*/
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package onlinestats
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import "math"
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type Running struct {
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n int
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m1, m2, m3, m4 float64
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}
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func NewRunning() *Running {
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return &Running{}
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}
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func (r *Running) Push(x float64) {
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n1 := float64(r.n)
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r.n++
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delta := x - r.m1
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delta_n := delta / float64(r.n)
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delta_n2 := delta_n * delta_n
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term1 := delta * delta_n * n1
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r.m1 += delta_n
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r.m4 += term1*delta_n2*float64(r.n*r.n-3*r.n+3) + 6*delta_n2*r.m2 - 4*delta_n*r.m3
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r.m3 += term1*delta_n*float64(r.n-2) - 3*delta_n*r.m2
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r.m2 += term1
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}
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func (r *Running) Len() int {
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return r.n
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}
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func (r *Running) Mean() float64 {
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return r.m1
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}
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func (r *Running) Var() float64 {
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return r.m2 / float64(r.n-1)
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}
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func (r *Running) Stddev() float64 {
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return math.Sqrt(r.Var())
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}
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func (r *Running) Skewness() float64 {
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return math.Sqrt(float64(r.n)) * r.m3 / math.Pow(r.m2, 1.5)
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}
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func (r *Running) Kurtosis() float64 {
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return float64(r.n)*r.m4/(r.m2*r.m2) - 3.0
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}
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func CombineRunning(a, b *Running) *Running {
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var combined Running
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an := float64(a.n)
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bn := float64(b.n)
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cn := float64(an + bn)
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combined.n = a.n + b.n
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delta := b.m1 - a.m1
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delta2 := delta * delta
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delta3 := delta * delta2
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delta4 := delta2 * delta2
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combined.m1 = (an*a.m1 + bn*b.m1) / cn
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combined.m2 = a.m2 + b.m2 + delta2*an*bn/cn
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combined.m3 = a.m3 + b.m3 + delta3*an*bn*(an-bn)/(cn*cn)
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combined.m3 += 3.0 * delta * (an*b.m2 - bn*a.m2) / cn
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combined.m4 = a.m4 + b.m4 + delta4*an*bn*(an*an-an*bn+bn*bn)/(cn*cn*cn)
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combined.m4 += 6.0*delta2*(an*an*b.m2+bn*bn*a.m2)/(cn*cn) + 4.0*delta*(an*b.m3-bn*a.m3)/cn
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return &combined
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}
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type Regression struct {
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xstats Running
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ystats Running
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sxy float64
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n int
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}
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func NewRegression() *Regression {
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return &Regression{}
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}
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func (r *Regression) Push(x, y float64) {
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r.sxy += (r.xstats.Mean() - x) * (r.ystats.Mean() - y) * float64(r.n) / float64(r.n+1)
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r.xstats.Push(x)
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r.ystats.Push(y)
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r.n++
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}
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func (r *Regression) Len() int {
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return r.n
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}
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func (r *Regression) Slope() float64 {
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sxx := r.xstats.Var() * float64(r.n-1)
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return r.sxy / sxx
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}
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func (r *Regression) Intercept() float64 {
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return r.ystats.Mean() - r.Slope()*r.xstats.Mean()
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}
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func (r *Regression) Correlation() float64 {
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t := r.xstats.Stddev() * r.ystats.Stddev()
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return r.sxy / (float64(r.n-1) * t)
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}
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func CombineRegressions(a, b Regression) *Regression {
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var combined Regression
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combined.xstats = *CombineRunning(&a.xstats, &b.xstats)
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combined.ystats = *CombineRunning(&a.ystats, &b.ystats)
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combined.n = a.n + b.n
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delta_x := b.xstats.Mean() - a.xstats.Mean()
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delta_y := b.ystats.Mean() - a.ystats.Mean()
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combined.sxy = a.sxy + b.sxy + float64(a.n*b.n)*delta_x*delta_y/float64(combined.n)
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return &combined
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}
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