route/vendor/github.com/dgryski/go-onlinestats/kstest.go

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package onlinestats
// https://en.wikipedia.org/wiki/Kolmogorov%E2%80%93Smirnov_test
// http://www.itl.nist.gov/div898/handbook/eda/section3/eda35g.htm
import (
"math"
"sort"
)
// From NR
// KS performs a Kolmogorov-Smirnov test for the two datasets, and returns the
// p-value for the null hypothesis that the two sets come from the same distribution.
func KS(data1, data2 []float64) float64 {
sort.Float64s(data1)
sort.Float64s(data2)
for math.IsNaN(data1[0]) {
data1 = data1[1:]
}
for math.IsNaN(data2[0]) {
data2 = data2[1:]
}
n1, n2 := len(data1), len(data2)
en1, en2 := float64(n1), float64(n2)
var d float64
var fn1, fn2 float64
j1, j2 := 0, 0
for j1 < n1 && j2 < n2 {
d1 := data1[j1]
d2 := data2[j2]
if d1 <= d2 {
for j1 < n1 && d1 == data1[j1] {
j1++
fn1 = float64(j1) / en1
}
}
if d2 <= d1 {
for j2 < n2 && d2 == data2[j2] {
j2++
fn2 = float64(j2) / en2
}
}
if dt := math.Abs(fn2 - fn1); dt > d {
d = dt
}
}
en := math.Sqrt((en1 * en2) / (en1 + en2))
// R and Octave don't use this approximation that NR does
//return qks((en + 0.12 + 0.11/en) * d)
return qks(en * d)
}
func qks(z float64) float64 {
if z < 0. {
panic("bad z in qks")
}
if z == 0. {
return 1.
}
if z < 1.18 {
return 1. - pks(z)
}
x := math.Exp(-2. * (z * z))
return 2. * (x - math.Pow(x, 4) + math.Pow(x, 9))
}
func pks(z float64) float64 {
if z < 0. {
panic("bad z in KSdist")
}
if z == 0. {
return 0.
}
if z < 1.18 {
y := math.Exp(-1.23370055013616983 / (z * z))
return 2.25675833419102515 * math.Sqrt(-math.Log(y)) * (y + math.Pow(y, 9) + math.Pow(y, 25) + math.Pow(y, 49))
}
x := math.Exp(-2. * (z * z))
return 1. - 2.*(x-math.Pow(x, 4)+math.Pow(x, 9))
}