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gonum/stat/distuv/noncentralt_test.go
Fumin a9119bd313 distuv: add non-central t distribution
2025-11-02 11:43:05 +10:30

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// Copyright ©2025 The Gonum Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
package distuv
import (
"fmt"
"math"
"math/rand/v2"
"sort"
"testing"
"gonum.org/v1/gonum/floats/scalar"
)
func TestNoncentralTRand(t *testing.T) {
t.Parallel()
const (
n = 3e5
bins = 50
)
rsrc := rand.NewPCG(1, 1)
tests := []struct {
dist NoncentralT
tol float64
}{
{dist: NoncentralT{Nu: 58, Mu: 1.9364916731037085, Src: rsrc}, tol: 1e-2},
{dist: NoncentralT{Nu: 198, Mu: 7.0710678118654755, Src: rsrc}, tol: 1e-2},
}
for i, test := range tests {
t.Run(fmt.Sprintf("%d", i), func(t *testing.T) {
x := make([]float64, n)
generateSamples(x, test.dist)
sort.Float64s(x)
testRandLogProbContinuous(t, i, math.Inf(-1), x, test.dist, test.tol, bins)
})
}
}
func TestNoncentralTMoments(t *testing.T) {
t.Parallel()
tests := []struct {
dist NoncentralT
mean float64
variance float64
tol float64
}{
{dist: NoncentralT{Nu: 20, Mu: 23}, mean: 23.909902487370097, variance: 17.205451933342147, tol: 1e-13},
}
for i, test := range tests {
t.Run(fmt.Sprintf("%d", i), func(t *testing.T) {
mean := test.dist.Mean()
if !scalar.EqualWithinRel(mean, test.mean, test.tol) {
t.Errorf("{%f, %f}.Mean: got %f want %f", test.dist.Nu, test.dist.Mu, mean, test.mean)
}
variance := test.dist.Variance()
if !scalar.EqualWithinRel(variance, test.variance, test.tol) {
t.Errorf("{%f, %f}.Variance: got %f want %f", test.dist.Nu, test.dist.Mu, variance, test.variance)
}
})
}
}
func TestNoncentralTProb(t *testing.T) {
t.Parallel()
tests := []struct {
dist NoncentralT
x float64
p float64
tol float64
abs float64
}{
// Based on https://github.com/wch/r-source/blob/trunk/tests/reg-tests-2.R
{dist: NoncentralT{Nu: 10, Mu: 0}, x: 1.8, p: 0.08311638965387959, tol: 5e-12},
{dist: NoncentralT{Nu: 10, Mu: 0.0001}, x: 1.8, p: 0.0831297211093226, tol: 5e-12},
{dist: NoncentralT{Nu: 10, Mu: 1}, x: 1.8, p: 0.2665039326310101, tol: 5e-12},
{dist: NoncentralT{Nu: 10, Mu: -0.0001}, x: 1.8, p: 0.08310305960463463, tol: 5e-12},
{dist: NoncentralT{Nu: 10, Mu: -1}, x: 1.8, p: 0.01074629362995775, tol: 5e-12},
// Based on https://github.com/boostorg/math/blob/develop/test/test_nc_t.hpp
{dist: NoncentralT{Nu: 8, Mu: 12}, x: 12, p: 1.23532971542589493e-1, tol: 5e-12},
{dist: NoncentralT{Nu: 126, Mu: -2}, x: -4, p: 5.79793228936581470e-2, tol: 2e-11},
{dist: NoncentralT{Nu: 126, Mu: 2}, x: 4, p: 5.79793228936581470e-2, tol: 2e-11},
{dist: NoncentralT{Nu: 126, Mu: 2}, x: 0, p: 5.38839489063995713e-2, tol: 5e-12},
{dist: NoncentralT{Nu: 8, Mu: 16}, x: 0, p: 9.94670846108541165e-57, tol: 5e-12},
{dist: NoncentralT{Nu: 8, Mu: 16}, x: 0x1p-1022, p: 9.94670846108541165e-57, tol: 5e-12},
{dist: NoncentralT{Nu: 8, Mu: 16}, x: -0x1p-1022, p: 9.94670846108541165e-57, tol: 5e-12},
{dist: NoncentralT{Nu: 8, Mu: 16}, x: -0.125, p: 1.40958893993909266e-57, tol: 5e-12, abs: 1e-16},
{dist: NoncentralT{Nu: 8, Mu: 16}, x: -1e-16, p: 9.94670846108539523e-57, tol: 5e-12},
{dist: NoncentralT{Nu: 8, Mu: 16}, x: 1e-16, p: 9.94670846108542807e-57, tol: 5e-12},
{dist: NoncentralT{Nu: 8, Mu: 16}, x: 0.125, p: 8.78741270305645722e-56, tol: 5e-4},
// Custom tests, wanted values from the R language version 4.4.2.
{dist: NoncentralT{Nu: 58, Mu: 1.936492}, x: -0.3930852906078905, p: 0.02631178912036441, tol: 5e-12},
{dist: NoncentralT{Nu: 58, Mu: 1.936492}, x: 0.6553966734339551, p: 0.1756830868490319, tol: 5e-12},
{dist: NoncentralT{Nu: 58, Mu: 1.936492}, x: 1.498837237776003, p: 0.3591385592167584, tol: 5e-12},
{dist: NoncentralT{Nu: 58, Mu: 1.936492}, x: 1.944945574355751, p: 0.3908781127965009, tol: 5e-12},
{dist: NoncentralT{Nu: 58, Mu: 1.936492}, x: 2.369093423208461, p: 0.3534073785987947, tol: 5e-12},
{dist: NoncentralT{Nu: 58, Mu: 1.936492}, x: 3.290148485967974, p: 0.1615374126723982, tol: 5e-12},
{dist: NoncentralT{Nu: 58, Mu: 1.936492}, x: 4.469416864177883, p: 0.02264358202648499, tol: 5e-12},
{dist: NoncentralT{Nu: 58, Mu: 1.936492}, x: 0, p: 0.0609166161931202, tol: 5e-12},
}
for i, test := range tests {
t.Run(fmt.Sprintf("%d", i), func(t *testing.T) {
p := test.dist.Prob(test.x)
if !scalar.EqualWithinAbsOrRel(p, test.p, test.abs, test.tol) {
t.Errorf("{%f, %f}.Prob(%f): got %g want %g", test.dist.Nu, test.dist.Mu, test.x, p, test.p)
}
})
}
}
func TestNoncentralTCDF(t *testing.T) {
t.Parallel()
tests := []struct {
dist NoncentralT
x float64
cdf float64
tol float64
abs float64
}{
// Based on https://github.com/wch/r-source/blob/trunk/tests/reg-tests-2.R
{dist: NoncentralT{Nu: 10, Mu: 0}, x: 1.8, cdf: 0.9489738784326605, tol: 5e-12},
{dist: NoncentralT{Nu: 10, Mu: 0.0001}, x: 1.8, cdf: 0.948964072175642, tol: 5e-12},
{dist: NoncentralT{Nu: 10, Mu: 1}, x: 1.8, cdf: 0.7584267206837773, tol: 5e-12},
{dist: NoncentralT{Nu: 10, Mu: -0.0001}, x: 1.8, cdf: 0.9489836831935839, tol: 5e-12},
{dist: NoncentralT{Nu: 10, Mu: -1}, x: 1.8, cdf: 0.9949471996805094, tol: 5e-12},
// Based on https://github.com/boostorg/math/blob/develop/test/scipy_issue_14901.cpp
{dist: NoncentralT{Nu: 2, Mu: 2}, x: 0.05, cdf: 0.02528206132724582, tol: 5e-12},
{dist: NoncentralT{Nu: 1, Mu: 3}, x: 0.05, cdf: 0.00154456589169420, tol: 5e-11},
// Based on https://github.com/boostorg/math/blob/develop/test/scipy_issue_17916_nct.cpp
{dist: NoncentralT{Nu: 2, Mu: 482023264}, x: 2, cdf: 0, tol: 5e-12},
// Based on https://github.com/boostorg/math/blob/develop/test/test_nc_t.hpp
{dist: NoncentralT{Nu: 3, Mu: 1}, x: 2.34, cdf: 0.801888999613917, tol: 5e-12},
{dist: NoncentralT{Nu: 126, Mu: -2}, x: -4.33, cdf: 1.252846196792878e-2, tol: 5e-11},
{dist: NoncentralT{Nu: 20, Mu: 23}, x: 23, cdf: 0.460134400391924, tol: 5e-12},
{dist: NoncentralT{Nu: 20, Mu: 33}, x: 34, cdf: 0.532008386378725, tol: 5e-12},
{dist: NoncentralT{Nu: 12, Mu: 38}, x: 39, cdf: 0.495868184917805, tol: 5e-12},
{dist: NoncentralT{Nu: 12, Mu: 39}, x: 39, cdf: 0.446304024668836, tol: 5e-2},
{dist: NoncentralT{Nu: 200, Mu: 38}, x: 39, cdf: 0.666194209961795, tol: 5e-11},
{dist: NoncentralT{Nu: 200, Mu: 42}, x: 40, cdf: 0.179292265426085, tol: 2e-3},
{dist: NoncentralT{Nu: 2, Mu: 4}, x: 5, cdf: 0.532020698669953, tol: 5e-12},
{dist: NoncentralT{Nu: 8, Mu: 16}, x: 0, cdf: 6.388754400538087e-58, tol: 5e-12},
{dist: NoncentralT{Nu: 8, Mu: 16}, x: 0x1p-1022, cdf: 6.388754400538087e-58, tol: 5e-12},
{dist: NoncentralT{Nu: 8, Mu: 16}, x: -0x1p-1022, cdf: 6.388754400538087e-58, tol: 5e-12, abs: 1e-16},
{dist: NoncentralT{Nu: 8, Mu: 16}, x: -0.125, cdf: 1.018937769092816e-58, tol: 5e-12, abs: 1e-16},
{dist: NoncentralT{Nu: 8, Mu: 16}, x: -1e-16, cdf: 6.388754400538077e-58, tol: 5e-12, abs: 1e-16},
{dist: NoncentralT{Nu: 8, Mu: 16}, x: 1e-16, cdf: 6.388754400538097e-58, tol: 5e-12},
{dist: NoncentralT{Nu: 8, Mu: 16}, x: 0.125, cdf: 5.029904883914148e-57, tol: 1e-4},
{dist: NoncentralT{Nu: 8, Mu: 8.5}, x: -1, cdf: 6.174794808375702e-20, tol: 2e-5, abs: 1e-16},
// Custom tests, wanted values from the R language version 4.4.2.
{dist: NoncentralT{Nu: 58, Mu: 1.936492}, x: -0.3930852906078905, cdf: 0.01, tol: 5e-12},
{dist: NoncentralT{Nu: 58, Mu: 1.936492}, x: 0.6553966734339551, cdf: 0.1, tol: 5e-12},
{dist: NoncentralT{Nu: 58, Mu: 1.936492}, x: 1.498837237776003, cdf: 0.33, tol: 5e-12},
{dist: NoncentralT{Nu: 58, Mu: 1.936492}, x: 1.944945574355751, cdf: 0.5, tol: 5e-12},
{dist: NoncentralT{Nu: 58, Mu: 1.936492}, x: 2.369093423208461, cdf: 0.66, tol: 5e-12},
{dist: NoncentralT{Nu: 58, Mu: 1.936492}, x: 3.290148485967974, cdf: 0.9, tol: 5e-12},
{dist: NoncentralT{Nu: 58, Mu: 1.936492}, x: 4.469416864177883, cdf: 0.99, tol: 5e-12},
{dist: NoncentralT{Nu: 198, Mu: 3.535534}, x: 1.206434338714708, cdf: 0.01, tol: 5e-12},
{dist: NoncentralT{Nu: 198, Mu: 3.535534}, x: 2.248666397791987, cdf: 0.1, tol: 5e-12},
{dist: NoncentralT{Nu: 198, Mu: 3.535534}, x: 3.094270376888891, cdf: 0.33, tol: 5e-12},
{dist: NoncentralT{Nu: 198, Mu: 3.535534}, x: 3.54004668094423, cdf: 0.5, tol: 5e-12},
{dist: NoncentralT{Nu: 198, Mu: 3.535534}, x: 3.961130093860616, cdf: 0.66, tol: 5e-12},
{dist: NoncentralT{Nu: 198, Mu: 3.535534}, x: 4.860775618489509, cdf: 0.9, tol: 5e-12},
{dist: NoncentralT{Nu: 198, Mu: 3.535534}, x: 5.97083270110298, cdf: 0.99, tol: 5e-12},
{dist: NoncentralT{Nu: 10, Mu: 38.5}, x: 40, cdf: 0.5073909173564686, tol: 5e-3},
}
for i, test := range tests {
t.Run(fmt.Sprintf("%d", i), func(t *testing.T) {
cdf := test.dist.CDF(test.x)
if !scalar.EqualWithinAbsOrRel(cdf, test.cdf, test.abs, test.tol) {
t.Errorf("{Nu: %f, Mu: %f}.CDF(%f): got %g want %g", test.dist.Nu, test.dist.Mu, test.x, cdf, test.cdf)
}
})
}
}
func TestNoncentralTQuantile(t *testing.T) {
t.Parallel()
tests := []struct {
dist NoncentralT
x float64
cdf float64
tol float64
abs float64
}{
// Based on https://github.com/wch/r-source/blob/trunk/tests/reg-tests-2.R
{dist: NoncentralT{Nu: 10, Mu: 0}, x: 1.812461122811676, cdf: 0.95, tol: 5e-12},
{dist: NoncentralT{Nu: 10, Mu: 0.0001}, x: 1.812579296911650, cdf: 0.95, tol: 5e-12},
{dist: NoncentralT{Nu: 10, Mu: 1}, x: 3.041741814971971, cdf: 0.95, tol: 5e-12},
{dist: NoncentralT{Nu: 10, Mu: -0.0001}, x: 1.8123429496892811, cdf: 0.95, tol: 5e-12},
{dist: NoncentralT{Nu: 10, Mu: -1}, x: 0.6797901881827499, cdf: 0.95, tol: 5e-12},
// Based on https://github.com/boostorg/math/blob/develop/test/test_nc_t.hpp
{dist: NoncentralT{Nu: 3, Mu: 1}, x: 2.34, cdf: 0.801888999613917, tol: 5e-12},
{dist: NoncentralT{Nu: 126, Mu: -2}, x: -4.33, cdf: 1.252846196792878e-2, tol: 5e-11},
{dist: NoncentralT{Nu: 20, Mu: 23}, x: 23, cdf: 0.460134400391924, tol: 5e-12},
{dist: NoncentralT{Nu: 20, Mu: 33}, x: 34, cdf: 0.532008386378725, tol: 5e-12},
{dist: NoncentralT{Nu: 12, Mu: 38}, x: 39, cdf: 0.495868184917805, tol: 5e-12},
{dist: NoncentralT{Nu: 12, Mu: 39}, x: 39, cdf: 0.446304024668836, tol: 5e-2},
{dist: NoncentralT{Nu: 200, Mu: 38}, x: 39, cdf: 0.666194209961795, tol: 5e-11},
{dist: NoncentralT{Nu: 200, Mu: 42}, x: 40, cdf: 0.179292265426085, tol: 2e-3},
{dist: NoncentralT{Nu: 2, Mu: 4}, x: 5, cdf: 0.532020698669953, tol: 5e-12},
// Custom tests, wanted values from the R language version 4.4.2.
{dist: NoncentralT{Nu: 58, Mu: 1.936492}, x: -0.3930852906078905, cdf: 0.01, tol: 5e-12},
{dist: NoncentralT{Nu: 58, Mu: 1.936492}, x: 0.6553966734339551, cdf: 0.1, tol: 5e-12},
{dist: NoncentralT{Nu: 58, Mu: 1.936492}, x: 1.498837237776003, cdf: 0.33, tol: 5e-12},
{dist: NoncentralT{Nu: 58, Mu: 1.936492}, x: 1.944945574355751, cdf: 0.5, tol: 5e-12},
{dist: NoncentralT{Nu: 58, Mu: 1.936492}, x: 2.369093423208461, cdf: 0.66, tol: 5e-12},
{dist: NoncentralT{Nu: 58, Mu: 1.936492}, x: 3.290148485967974, cdf: 0.9, tol: 5e-12},
{dist: NoncentralT{Nu: 58, Mu: 1.936492}, x: 4.469416864177883, cdf: 0.99, tol: 5e-12},
{dist: NoncentralT{Nu: 198, Mu: 3.535534}, x: 1.206434338714708, cdf: 0.01, tol: 5e-12},
{dist: NoncentralT{Nu: 198, Mu: 3.535534}, x: 2.248666397791987, cdf: 0.1, tol: 5e-12},
{dist: NoncentralT{Nu: 198, Mu: 3.535534}, x: 3.094270376888891, cdf: 0.33, tol: 5e-12},
{dist: NoncentralT{Nu: 198, Mu: 3.535534}, x: 3.54004668094423, cdf: 0.5, tol: 5e-12},
{dist: NoncentralT{Nu: 198, Mu: 3.535534}, x: 3.961130093860616, cdf: 0.66, tol: 5e-12},
{dist: NoncentralT{Nu: 198, Mu: 3.535534}, x: 4.860775618489509, cdf: 0.9, tol: 5e-12},
{dist: NoncentralT{Nu: 198, Mu: 3.535534}, x: 5.97083270110298, cdf: 0.99, tol: 5e-12},
}
for i, test := range tests {
t.Run(fmt.Sprintf("%d", i), func(t *testing.T) {
x := test.dist.Quantile(test.cdf)
if !scalar.EqualWithinAbsOrRel(x, test.x, test.abs, test.tol) {
t.Errorf("{Nu: %f, Mu: %f}.Quantile(%f): got %g want %g", test.dist.Nu, test.dist.Mu, test.cdf, x, test.x)
}
})
}
}
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