func checkQuantileCDFSurvival(t *testing.T, i int, xs []float64, c cumulanter, tol float64) {
// Quantile, CDF, and survival check.
for i, p := range []float64{0.1, 0.25, 0.5, 0.75, 0.9} {
x := c.Quantile(p)
cdf := c.CDF(x)
estCDF := stat.CDF(x, stat.Empirical, xs, nil)
if !floats.EqualWithinAbsOrRel(cdf, estCDF, tol, tol) {
t.Errorf("CDF mismatch case %v: want: %v, got: %v", i, estCDF, cdf)
}
if !floats.EqualWithinAbsOrRel(cdf, p, tol, tol) {
t.Errorf("Quantile/CDF mismatch case %v: want: %v, got: %v", i, p, cdf)
}
if math.Abs(1-cdf-c.Survival(x)) > 1e-14 {
t.Errorf("Survival/CDF mismatch case %v: want: %v, got: %v", i, 1-cdf, c.Survival(x))
}
}
}
// checkProbQuantContinuous checks that the Prob, Rand, and Quantile are all consistent.
// checkProbContinuous only checks that Prob is a valid distribution (integrates
// to 1 and greater than 0). However, this is also true if the PDF of a different
// distribution is used. This checks that PDF is also consistent with the
// CDF implementation and the random samples.
func checkProbQuantContinuous(t *testing.T, i int, xs []float64, c cumulantProber, tol float64) {
ps := make([]float64, 101)
floats.Span(ps, 0, 1)
var xp, x float64
for i, p := range ps {
x = c.Quantile(p)
if p == 0 {
xp = x
if floats.Min(xs) < x {
t.Errorf("Sample of x less than Quantile(0). Case %v.", i)
break
}
continue
}
if p == 1 {
if floats.Max(xs) > x {
t.Errorf("Sample of x greater than Quantile(1). Case %v.", i)
break
}
}
// The integral of the PDF between xp and x should be the difference in
// the quantiles.
q := quad.Fixed(c.Prob, xp, x, 1000, nil, 0)
if math.Abs(q-(p-ps[i-1])) > 1e-10 {
t.Errorf("Integral of PDF doesn't match quantile. Case %v. Want %v, got %v.", i, p-ps[i-1], q)
break
}
pEst := stat.CDF(x, stat.Empirical, xs, nil)
if math.Abs(pEst-p) > tol {
t.Errorf("Empirical CDF doesn't match quantile. Case %v.", i)
}
xp = x
}
}
// testFullDist tests all of the functions of a fullDist.
func testFullDist(t *testing.T, f fullDist, i int) {
tol := 1e-1
const n = 1e6
xs := make([]float64, n)
for i := range xs {
xs[i] = f.Rand()
}
sortedXs := make([]float64, n)
copy(sortedXs, xs)
sort.Float64s(sortedXs)
tmp := make([]float64, n)
// Mean check.
mean := stat.Mean(xs, nil)
if !floats.EqualWithinAbsOrRel(mean, f.Mean(), tol, tol) {
t.Errorf("Mean mismatch case %v: want: %v, got: %v", i, mean, f.Mean())
} else {
mean = f.Mean()
}
// Median check.
median := stat.Quantile(0.5, stat.Empirical, sortedXs, nil)
if !floats.EqualWithinAbsOrRel(median, f.Median(), tol, tol) {
t.Errorf("Median mismatch case %v: want: %v, got: %v", i, median, f.Median())
}
// Variance check.
variance := stat.Variance(xs, nil)
if !floats.EqualWithinAbsOrRel(variance, f.Variance(), tol, tol) {
t.Errorf("Variance mismatch case %v: want: %v, got: %v", i, mean, f.Variance())
} else {
variance = f.Variance()
}
std := math.Sqrt(variance)
if !floats.EqualWithinAbsOrRel(std, f.StdDev(), tol, tol) {
t.Errorf("StdDev mismatch case %v: want: %v, got: %v", i, mean, f.StdDev())
} else {
std = f.StdDev()
}
// Entropy check.
for i, x := range xs {
tmp[i] = -f.LogProb(x)
}
entropy := stat.Mean(tmp, nil)
if !floats.EqualWithinAbsOrRel(entropy, f.Entropy(), tol, tol) {
t.Errorf("Entropy mismatch case %v: want: %v, got: %v", i, entropy, f.Entropy())
}
// Excess Kurtosis check.
for i, x := range xs {
tmp[i] = math.Pow(x-mean, 4)
}
mu4 := stat.Mean(tmp, nil)
kurtosis := mu4/(variance*variance) - 3
if !floats.EqualWithinAbsOrRel(kurtosis, f.ExKurtosis(), tol, tol) {
t.Errorf("ExKurtosis mismatch case %v: want: %v, got: %v", i, kurtosis, f.ExKurtosis())
}
// Skewness check.
for i, x := range xs {
tmp[i] = math.Pow(x-mean, 3)
}
mu3 := stat.Mean(tmp, nil)
skewness := mu3 / math.Pow(std, 3)
if !floats.EqualWithinAbsOrRel(skewness, f.Skewness(), tol, tol) {
t.Errorf("ExKurtosis mismatch case %v: want: %v, got: %v", i, skewness, f.Skewness())
}
// Quantile, CDF, and survival check.
for i, p := range []float64{0.1, 0.25, 0.5, 0.75, 0.9} {
x := f.Quantile(p)
cdf := f.CDF(x)
estCDF := stat.CDF(x, stat.Empirical, sortedXs, nil)
if !floats.EqualWithinAbsOrRel(cdf, estCDF, tol, tol) {
t.Errorf("CDF mismatch case %v: want: %v, got: %v", i, estCDF, cdf)
}
if !floats.EqualWithinAbsOrRel(cdf, p, tol, tol) {
t.Errorf("Quantile/CDF mismatch case %v: want: %v, got: %v", i, p, cdf)
}
if math.Abs(1-cdf-f.Survival(x)) > 1e-14 {
t.Errorf("Survival/CDF mismatch case %v: want: %v, got: %v", i, 1-cdf, f.Survival(x))
}
}
// Prob and LogProb check.
m := 1001
bins := make([]float64, m)
dividers := make([]float64, m)
floats.Span(bins, 0, 1)
for i, v := range bins {
dividers[i] = f.Quantile(v)
}
counts := stat.Histogram(nil, dividers, sortedXs, nil)
// Test PDf against normalized count
for i, v := range counts {
v /= float64(n)
at := f.Quantile((bins[i] + bins[i+1]) / 2)
prob := f.Prob(at)
if !floats.EqualWithinAbsOrRel(skewness, f.Skewness(), tol, tol) {
t.Errorf("Prob mismatch case %v at %v: want: %v, got: %v", i, at, v, prob)
break
}
if math.Abs(math.Log(prob)-f.LogProb(at)) > 1e-14 {
t.Errorf("Prob and LogProb mismatch case %v at %v: want %v, got %v", i, at, math.Log(prob), f.LogProb(at))
break
}
}
}