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Add Normal Distribution Functions (#56)

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rvchess authored and montanaflynn committed Jan 22, 2020
1 parent 7479779 commit 60d707fd1db41538718d32aa9f0ea667a62716c2
Showing with 479 additions and 0 deletions.
  1. +19 −0 README.md
  2. +256 −0 norm.go
  3. +204 −0 norm_test.go
@@ -89,6 +89,25 @@ func Midhinge(input Float64Data) (float64, error) {}
func Min(input Float64Data) (min float64, err error) {}
func MinkowskiDistance(dataPointX, dataPointY Float64Data, lambda float64) (distance float64, err error) {}
func Mode(input Float64Data) (mode []float64, err error) {}
func NormBoxMullerRvs(loc float64, scale float64, size int) []float64 {}
func NormCdf(x float64, loc float64, scale float64) float64 {}
func NormEntropy(loc float64, scale float64) float64 {}
func NormFit(data []float64) [2]float64{}
func NormInterval(alpha float64, loc float64, scale float64 ) [2]float64 {}
func NormIsf(p float64, loc float64, scale float64) (x float64) {}
func NormLogCdf(x float64, loc float64, scale float64) float64 {}
func NormLogPdf(x float64, loc float64, scale float64) float64 {}
func NormLogSf(x float64, loc float64, scale float64) float64 {}
func NormMean(loc float64, scale float64) float64 {}
func NormMedian(loc float64, scale float64) float64 {}
func NormMoment(n int, loc float64, scale float64) float64 {}
func NormPdf(x float64, loc float64, scale float64) float64 {}
func NormPpf(p float64, loc float64, scale float64) (x float64) {}
func NormPpfRvs(loc float64, scale float64, size int) []float64 {}
func NormSf(x float64, loc float64, scale float64) float64 {}
func NormStats(loc float64, scale float64, moments string) []float64 {}
func NormStd(loc float64, scale float64) float64 {}
func NormVar(loc float64, scale float64) float64 {}
func Pearson(data1, data2 Float64Data) (float64, error) {}
func Percentile(input Float64Data, percent float64) (percentile float64, err error) {}
func PercentileNearestRank(input Float64Data, percent float64) (percentile float64, err error) {}
256 norm.go
@@ -0,0 +1,256 @@
package stats

import (
"math"
"math/rand"
"strings"
"time"
)

// NormPpfRvs generates random variates using the Point Percentile Function.
// For more information please visit: https://demonstrations.wolfram.com/TheMethodOfInverseTransforms/
func NormPpfRvs(loc float64, scale float64, size int) []float64 {
rand.Seed(time.Now().UnixNano())
var toReturn []float64
for i := 0; i < size; i++ {
toReturn = append(toReturn, NormPpf(rand.Float64(), loc, scale))
}
return toReturn
}

// NormBoxMullerRvs generates random variates using the Box–Muller transform.
// For more information please visit: http://mathworld.wolfram.com/Box-MullerTransformation.html
func NormBoxMullerRvs(loc float64, scale float64, size int) []float64 {
rand.Seed(time.Now().UnixNano())
var toReturn []float64
for i := 0; i < int(math.Floor(float64(size / 2)) + float64(size % 2)); i++ {
// u1 and u2 are uniformly distributed random numbers between 0 and 1.
u1 := rand.Float64()
u2 := rand.Float64()
// x1 and x2 are normally distributed random numbers.
x1 := loc + (scale * (math.Sqrt(-2*math.Log(u1)) * math.Cos(2*math.Pi*u2)))
toReturn = append(toReturn, x1)
if (i + 1) * 2 <= size {
x2 := loc + (scale * (math.Sqrt(-2*math.Log(u1)) * math.Sin(2*math.Pi*u2)))
toReturn = append(toReturn, x2)
}
}
return toReturn
}

// NormPdf is the probability density function.
func NormPdf(x float64, loc float64, scale float64) float64 {
return (math.Pow(math.E, -(math.Pow(x-loc, 2)) / (2 * math.Pow(scale, 2)))) / (scale* math.Sqrt(2 * math.Pi))
}

// NormLogPdf is the log of the probability density function.
func NormLogPdf(x float64, loc float64, scale float64) float64 {
return math.Log((math.Pow(math.E, -(math.Pow(x-loc, 2)) / (2 * math.Pow(scale, 2)))) / (scale* math.Sqrt(2 * math.Pi)))
}

// NormCdf is the cumulative distribution function.
func NormCdf(x float64, loc float64, scale float64) float64 {
return 0.5*(1 + math.Erf((x - loc) / (scale * math.Sqrt(2))))
}

// NormLogCdf is the log of the cumulative distribution function.
func NormLogCdf(x float64, loc float64, scale float64) float64 {
return math.Log(0.5*(1 + math.Erf((x - loc) / (scale * math.Sqrt(2)))))
}

// NormSf is the survival function (also defined as 1 - cdf, but sf is sometimes more accurate).
func NormSf(x float64, loc float64, scale float64) float64 {
return 1 - 0.5*(1 + math.Erf((x - loc) / (scale * math.Sqrt(2))))
}

// NormLogSf is the log of the survival function.
func NormLogSf(x float64, loc float64, scale float64) float64 {
return math.Log(1 - 0.5*(1 + math.Erf((x - loc) / (scale * math.Sqrt(2)))))
}

// NormPpf is the point percentile function.
// This is based on Peter John Acklam's inverse normal CDF.
// algorithm: http://home.online.no/~pjacklam/notes/invnorm/ (no longer visible).
// For more information please visit: https://stackedboxes.org/2017/05/01/acklams-normal-quantile-function/
func NormPpf(p float64, loc float64, scale float64) (x float64) {
const (
a1 = -3.969683028665376e+01
a2 = 2.209460984245205e+02
a3 = -2.759285104469687e+02
a4 = 1.383577518672690e+02
a5 = -3.066479806614716e+01
a6 = 2.506628277459239e+00

b1 = -5.447609879822406e+01
b2 = 1.615858368580409e+02
b3 = -1.556989798598866e+02
b4 = 6.680131188771972e+01
b5 = -1.328068155288572e+01

c1 = -7.784894002430293e-03
c2 = -3.223964580411365e-01
c3 = -2.400758277161838e+00
c4 = -2.549732539343734e+00
c5 = 4.374664141464968e+00
c6 = 2.938163982698783e+00

d1 = 7.784695709041462e-03
d2 = 3.224671290700398e-01
d3 = 2.445134137142996e+00
d4 = 3.754408661907416e+00

plow = 0.02425
phigh = 1 - plow
)

if p < 0 || p > 1 {
return math.NaN()
} else if p == 0 {
return -math.Inf(0)
} else if p == 1 {
return math.Inf(0)
}

if p < plow {
q := math.Sqrt(-2 * math.Log(p))
x = (((((c1*q+c2)*q+c3)*q+c4)*q+c5)*q + c6) /
((((d1*q+d2)*q+d3)*q+d4)*q + 1)
} else if phigh < p {
q := math.Sqrt(-2 * math.Log(1-p))
x = -(((((c1*q+c2)*q+c3)*q+c4)*q+c5)*q + c6) /
((((d1*q+d2)*q+d3)*q+d4)*q + 1)
} else {
q := p - 0.5
r := q * q
x = (((((a1*r+a2)*r+a3)*r+a4)*r+a5)*r + a6) * q /
(((((b1*r+b2)*r+b3)*r+b4)*r+b5)*r + 1)
}

e := 0.5*math.Erfc(-x/math.Sqrt2) - p
u := e * math.Sqrt(2*math.Pi) * math.Exp(x*x/2)
x = x - u/(1+x*u/2)

return x*scale + loc
}

// NormIsf is the inverse survival function (inverse of sf).
func NormIsf(p float64, loc float64, scale float64) (x float64) {
if -NormPpf(p, loc, scale) == 0 {
return 0
}
return -NormPpf(p, loc, scale)
}

// NormMoment approximates the non-central (raw) moment of order n.
// For more information please visit: https://math.stackexchange.com/questions/1945448/methods-for-finding-raw-moments-of-the-normal-distribution
func NormMoment(n int, loc float64, scale float64) float64 {
toReturn := 0.0
for i := 0; i < n + 1; i++ {
if (n-i) % 2 == 0 {
toReturn += float64(Ncr(n, i)) * (math.Pow(loc, float64(i))) * (math.Pow(scale, float64(n - i))) *
(float64(factorial(n - i)) / ((math.Pow(2.0, float64((n - i) / 2))) *
float64(factorial((n - i) / 2))))
}
}
return toReturn
}
// NormStats returns the mean, variance, skew, and/or kurtosis.
// Mean(‘m’), variance(‘v’), skew(‘s’), and/or kurtosis(‘k’).
// Takes string containing any of 'mvsk'.
// Returns array of m v s k in that order.
func NormStats(loc float64, scale float64, moments string) []float64 {
var toReturn []float64
if strings.ContainsAny(moments, "m") {
toReturn = append(toReturn, loc)
}
if strings.ContainsAny(moments, "v") {
toReturn = append(toReturn, math.Pow(scale, 2))
}
if strings.ContainsAny(moments, "s") {
toReturn = append(toReturn, 0.0)
}
if strings.ContainsAny(moments, "k") {
toReturn = append(toReturn, 0.0)
}
return toReturn
}

// NormEntropy is the differential entropy of the RV.
func NormEntropy(loc float64, scale float64) float64 {
return math.Log(scale * math.Sqrt(2 * math.Pi * math.E))
}

// NormFit returns the maximum likelihood estimators for the Normal Distribution.
// Takes array of float64 values.
// Returns array of Mean followed by Standard Deviation.
func NormFit(data []float64) [2]float64{
sum := 0.00
mean := 0.00
for i := 0; i < len(data); i++ {
sum += data[i]
}
mean = sum / float64(len(data))
stdNumerator := 0.00
for i := 0; i < len(data); i++ {
stdNumerator += math.Pow(data[i]-mean, 2)
}
return [2]float64{mean , math.Sqrt((stdNumerator)/(float64(len(data))))}
}

// NormMedian is the median of the distribution.
func NormMedian(loc float64, scale float64) float64 {
return loc
}

// NormMean is the mean/expected value of the distribution.
func NormMean(loc float64, scale float64) float64 {
return loc
}

// NormVar is the variance of the distribution.
func NormVar(loc float64, scale float64) float64 {
return math.Pow(scale, 2)
}

// NormStd is the standard deviation of the distribution.
func NormStd(loc float64, scale float64) float64 {
return scale
}

// NormInterval finds endpoints of the range that contains alpha percent of the distribution.
func NormInterval(alpha float64, loc float64, scale float64 ) [2]float64 {
q1 := (1.0-alpha)/2
q2 := (1.0+alpha)/2
a := NormPpf(q1, loc, scale)
b := NormPpf(q2, loc, scale)
return [2]float64{a, b}
}

// factorial is the naive factorial algorithm.
func factorial(x int) int {
if x == 0 {
return 1
}
return x * factorial(x - 1)
}

// Ncr is an N choose R algorithm.
// Aaron Cannon's algorithm.
func Ncr(n, r int) int {
if n <= 1 || r == 0 || n == r {
return 1
}
if newR := n - r; newR < r {
r = newR
}
if r == 1 {
return n
}
ret := int(n - r + 1)
for i, j := ret+1, int(2); j <= r; i, j = i+1, j+1 {
ret = ret * i / j
}
return ret
}


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