stat: add support for LinInterp CumulantKind for Quantile

stat/stat.go

@@ -20,6 +20,8 @@ type CumulantKind int
 const (
 	// Empirical treats the distribution as the actual empirical distribution.
 	Empirical CumulantKind = 1
+	// LinInterp linearly interpolates the empirical distribution between sample values, with a flat extrapolation.
+	LinInterp CumulantKind = 4
 )
 
 // bhattacharyyaCoeff computes the Bhattacharyya Coefficient for probability distributions given by:
@@ -1028,6 +1030,7 @@ func MomentAbout(moment float64, x []float64, mean float64, weights []float64) f
 // CumulantKind behaviors:
 //  - Empirical: Returns the lowest value q for which q is greater than or equal
 //  to the fraction p of samples
+//  - LinInterp: Returns the linearly interpolated value
 func Quantile(p float64, c CumulantKind, x, weights []float64) float64 {
 	if !(p >= 0 && p <= 1) {
 		panic("stat: percentile out of bounds")
@@ -1052,6 +1055,8 @@ func Quantile(p float64, c CumulantKind, x, weights []float64) float64 {
 	switch c {
 	case Empirical:
 		return empiricalQuantile(p, x, weights, sumWeights)
+	case LinInterp:
+		return linInterpQuantile(p, x, weights, sumWeights)
 	default:
 		panic("stat: bad cumulant kind")
 	}
@@ -1073,6 +1078,29 @@ func empiricalQuantile(p float64, x, weights []float64, sumWeights float64) floa
 	panic("impossible")
 }
 
+func linInterpQuantile(p float64, x, weights []float64, sumWeights float64) float64 {
+	var cumsum float64
+	fidx := p * sumWeights
+	for i := range x {
+		if weights == nil {
+			cumsum++
+		} else {
+			cumsum += weights[i]
+		}
+		if cumsum >= fidx {
+			if i == 0 {
+				return x[0]
+			}
+			t := cumsum - fidx
+			if weights != nil {
+				t /= weights[i]
+			}
+			return t*x[i-1] + (1-t)*x[i]
+		}
+	}
+	panic("impossible")
+}
+
 // Skew computes the skewness of the sample data.
 // If weights is nil then all of the weights are 1. If weights is not nil, then
 // len(x) must equal len(weights).

stat/stat_test.go

@@ -1423,7 +1423,10 @@ func TestCDF(t *testing.T) {
 }
 
 func TestQuantile(t *testing.T) {
-	cumulantKinds := []CumulantKind{Empirical}
+	cumulantKinds := []CumulantKind{
+		Empirical,
+		LinInterp,
+	}
 	for i, test := range []struct {
 		p   []float64
 		x   []float64
@@ -1431,21 +1434,39 @@ func TestQuantile(t *testing.T) {
 		ans [][]float64
 	}{
 		{
-			p:   []float64{0, 0.05, 0.1, 0.15, 0.45, 0.5, 0.55, 0.85, 0.9, 0.95, 1},
+			p: []float64{0, 0.05, 0.1, 0.15, 0.45, 0.5, 0.55, 0.85, 0.9, 0.95, 1},
-			x:   []float64{1, 2, 3, 4, 5, 6, 7, 8, 9, 10},
+			x: []float64{1, 2, 3, 4, 5, 6, 7, 8, 9, 10},
-			w:   nil,
+			w: nil,
-			ans: [][]float64{{1, 1, 1, 2, 5, 5, 6, 9, 9, 10, 10}},
+			ans: [][]float64{
+				{1, 1, 1, 2, 5, 5, 6, 9, 9, 10, 10},
+				{1, 1, 1, 1.5, 4.5, 5, 5.5, 8.5, 9, 9.5, 10},
+			},
 		},
 		{
-			p:   []float64{0, 0.05, 0.1, 0.15, 0.45, 0.5, 0.55, 0.85, 0.9, 0.95, 1},
+			p: []float64{0, 0.05, 0.1, 0.15, 0.45, 0.5, 0.55, 0.85, 0.9, 0.95, 1},
-			x:   []float64{1, 2, 3, 4, 5, 6, 7, 8, 9, 10},
+			x: []float64{1, 2, 3, 4, 5, 6, 7, 8, 9, 10},
-			w:   []float64{3, 3, 3, 3, 3, 3, 3, 3, 3, 3},
+			w: []float64{3, 3, 3, 3, 3, 3, 3, 3, 3, 3},
-			ans: [][]float64{{1, 1, 1, 2, 5, 5, 6, 9, 9, 10, 10}},
+			ans: [][]float64{
+				{1, 1, 1, 2, 5, 5, 6, 9, 9, 10, 10},
+				{1, 1, 1, 1.5, 4.5, 5, 5.5, 8.5, 9, 9.5, 10},
+			},
 		},
 		{
-			p:   []float64{0.5},
+			p: []float64{0, 0.05, 0.1, 0.15, 0.45, 0.5, 0.55, 0.85, 0.9, 0.95, 1},
-			x:   []float64{1, 2, 3, 4, 5, 6, 7, 8, math.NaN(), 10},
+			x: []float64{1, 2, 3, 4, 5, 6, 7, 8, 9, 10},
-			ans: [][]float64{{math.NaN()}},
+			w: []float64{0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0},
+			ans: [][]float64{
+				{1, 2, 3, 4, 7, 7, 8, 10, 10, 10, 10},
+				{1, 1.875, 2.833333333333333, 3.5625, 6.535714285714286, 6.928571428571429, 7.281250000000001, 9.175, 9.45, 9.725, 10},
+			},
+		},
+		{
+			p: []float64{0.5},
+			x: []float64{1, 2, 3, 4, 5, 6, 7, 8, math.NaN(), 10},
+			ans: [][]float64{
+				{math.NaN()},
+				{math.NaN()},
+			},
 		},
 	} {
 		copyX := make([]float64, len(test.x))
@@ -1470,55 +1491,57 @@ func TestQuantile(t *testing.T) {
 			}
 		}
 	}
-	// panic cases
+}
+
+func TestQuantileInvalidInput(t *testing.T) {
+	cumulantKinds := []CumulantKind{
+		Empirical,
+		LinInterp,
+	}
 	for _, test := range []struct {
 		name string
 		p    float64
-		c    CumulantKind
 		x    []float64
 		w    []float64
 	}{
 		{
 			name: "p < 0",
-			c:    Empirical,
 			p:    -1,
 		},
 		{
 			name: "p > 1",
-			c:    Empirical,
 			p:    2,
 		},
 		{
 			name: "p is NaN",
-			c:    Empirical,
 			p:    math.NaN(),
 		},
 		{
 			name: "len(x) != len(weights)",
-			c:    Empirical,
 			p:    .5,
 			x:    make([]float64, 4),
 			w:    make([]float64, 2),
 		},
 		{
 			name: "x not sorted",
-			c:    Empirical,
 			p:    .5,
 			x:    []float64{3, 2, 1},
 		},
-		{
-			name: "CumulantKind is unknown",
-			c:    CumulantKind(1000),
-			p:    .5,
-			x:    []float64{1, 2, 3},
-		},
 	} {
-		if !panics(func() { Quantile(test.p, test.c, test.x, test.w) }) {
+		for _, kind := range cumulantKinds {
-			t.Errorf("Quantile did not panic when %s", test.name)
+			if !panics(func() { Quantile(test.p, kind, test.x, test.w) }) {
+				t.Errorf("Quantile did not panic when %s", test.name)
+			}
 		}
 	}
 }
 
+func TestQuantileInvalidCumulantKind(t *testing.T) {
+	if !panics(func() { Quantile(0.5, CumulantKind(1000), []float64{1, 2, 3}, nil) }) {
+		t.Errorf("Quantile did not panic when CumulantKind is unknown")
+	}
+}
+
 func ExampleStdDev() {
 	x := []float64{8, 2, -9, 15, 4}
 	stdev := StdDev(x, nil)