// Fit sets the parameters of the probability distribution from the
// data samples x with relative weights w.
// If weights is nil, then all the weights are 1.
// If weights is not nil, then the len(weights) must equal len(samples).
//
// Note: Laplace distribution has no FitPrior because it has no sufficient
// statistics.
func (l *Laplace) Fit(samples, weights []float64) {
if len(samples) != len(weights) {
panic(badLength)
}
if len(samples) == 0 {
panic(badNoSamples)
}
if len(samples) == 1 {
l.Mu = samples[0]
l.Scale = 0
return
}
var (
sortedSamples []float64
sortedWeights []float64
)
if sort.Float64sAreSorted(samples) {
sortedSamples = samples
sortedWeights = weights
} else {
// Need to copy variables so the input variables aren't effected by the sorting
sortedSamples = make([]float64, len(samples))
copy(sortedSamples, samples)
sortedWeights := make([]float64, len(samples))
copy(sortedWeights, weights)
stat.SortWeighted(sortedSamples, sortedWeights)
}
// The (weighted) median of the samples is the maximum likelihood estimate
// of the mean parameter
// TODO: Rethink quantile type when stat has more options
l.Mu = stat.Quantile(0.5, stat.Empirical, sortedSamples, sortedWeights)
sumWeights := floats.Sum(weights)
// The scale parameter is the average absolute distance
// between the sample and the mean
absError := stat.MomentAbout(1, samples, l.Mu, weights)
l.Scale = absError / sumWeights
}
// 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
}
}
}
func checkMedian(t *testing.T, i int, x []float64, m medianer, tol float64) {
median := stat.Quantile(0.5, stat.Empirical, x, nil)
if !floats.EqualWithinAbsOrRel(median, m.Median(), tol, tol) {
t.Errorf("Median mismatch case %v: want: %v, got: %v", i, median, m.Median())
}
}
