diff --git a/ext/stats/boolean.go b/ext/stats/boolean.go
index ba0ed69..f30fa07 100644
--- a/ext/stats/boolean.go
+++ b/ext/stats/boolean.go
@@ -26,21 +26,21 @@ func (b *boolean) Value(ctx sqlite3.Context) {
 }
 
 func (b *boolean) Step(ctx sqlite3.Context, arg ...sqlite3.Value) {
-	if arg[0].Type() == sqlite3.NULL {
-		return
-	}
-	if arg[0].Bool() {
+	a := arg[0]
+	if a.Bool() {
 		b.count++
 	}
-	b.total++
+	if a.Type() != sqlite3.NULL {
+		b.total++
+	}
 }
 
 func (b *boolean) Inverse(ctx sqlite3.Context, arg ...sqlite3.Value) {
-	if arg[0].Type() == sqlite3.NULL {
-		return
-	}
-	if arg[0].Bool() {
+	a := arg[0]
+	if a.Bool() {
 		b.count--
 	}
-	b.total--
+	if a.Type() != sqlite3.NULL {
+		b.total--
+	}
 }
diff --git a/ext/stats/percentile.go b/ext/stats/percentile.go
index 68646f8..2999b56 100644
--- a/ext/stats/percentile.go
+++ b/ext/stats/percentile.go
@@ -40,8 +40,14 @@ func (q *percentile) Step(ctx sqlite3.Context, arg ...sqlite3.Value) {
 }
 
 func (q *percentile) Inverse(ctx sqlite3.Context, arg ...sqlite3.Value) {
-	// Implementing inverse allows certain queries that don't really need it to succeed.
-	ctx.ResultError(util.ErrorString("percentile: may not be used as a window function"))
+	a := arg[0]
+	f := a.Float()
+	if f != 0.0 || a.NumericType() != sqlite3.NULL {
+		i := slices.Index(q.nums, f)
+		l := len(q.nums) - 1
+		q.nums[i] = q.nums[l]
+		q.nums = q.nums[:l]
+	}
 }
 
 func (q *percentile) Value(ctx sqlite3.Context) {
@@ -55,13 +61,13 @@ func (q *percentile) Value(ctx sqlite3.Context) {
 		floats []float64
 	)
 	if q.kind == median {
-		float, err = getPercentile(q.nums, 0.5, q.kind)
+		float, err = q.at(0.5)
 		ctx.ResultFloat(float)
 	} else if err = json.Unmarshal(q.arg1, &float); err == nil {
-		float, err = getPercentile(q.nums, float, q.kind)
+		float, err = q.at(float)
 		ctx.ResultFloat(float)
 	} else if err = json.Unmarshal(q.arg1, &floats); err == nil {
-		err = getPercentiles(q.nums, floats, q.kind)
+		err = q.atMore(floats)
 		ctx.ResultJSON(floats)
 	}
 	if err != nil {
@@ -69,28 +75,28 @@ func (q *percentile) Value(ctx sqlite3.Context) {
 	}
 }
 
-func getPercentile(nums []float64, pos float64, kind int) (float64, error) {
-	if kind == percentile_100 {
+func (q *percentile) at(pos float64) (float64, error) {
+	if q.kind == percentile_100 {
 		pos = pos / 100
 	}
 	if pos < 0 || pos > 1 {
 		return 0, util.ErrorString("invalid pos")
 	}
 
-	i, f := math.Modf(pos * float64(len(nums)-1))
-	m0 := quick.Select(nums, int(i))
+	i, f := math.Modf(pos * float64(len(q.nums)-1))
+	m0 := quick.Select(q.nums, int(i))
 
-	if f == 0 || kind == percentile_disc {
+	if f == 0 || q.kind == percentile_disc {
 		return m0, nil
 	}
 
-	m1 := slices.Min(nums[int(i)+1:])
+	m1 := slices.Min(q.nums[int(i)+1:])
 	return math.FMA(f, m1, math.FMA(-f, m0, m0)), nil
 }
 
-func getPercentiles(nums []float64, pos []float64, kind int) error {
+func (q *percentile) atMore(pos []float64) error {
 	for i := range pos {
-		v, err := getPercentile(nums, pos[i], kind)
+		v, err := q.at(pos[i])
 		if err != nil {
 			return err
 		}
diff --git a/ext/stats/percentile_test.go b/ext/stats/percentile_test.go
index 41f2e8b..985f10e 100644
--- a/ext/stats/percentile_test.go
+++ b/ext/stats/percentile_test.go
@@ -58,6 +58,40 @@ func TestRegister_percentile(t *testing.T) {
 	}
 	stmt.Close()
 
+	stmt, _, err = db.Prepare(`
+		SELECT
+			median(x) OVER (ROWS BETWEEN 1 PRECEDING AND 1 FOLLOWING)
+		FROM data`)
+	if err != nil {
+		t.Fatal(err)
+	}
+	if stmt.Step() {
+		if got := stmt.ColumnFloat(0); got != 5.5 {
+			t.Errorf("got %v, want 5.5", got)
+		}
+	}
+	if stmt.Step() {
+		if got := stmt.ColumnFloat(0); got != 7 {
+			t.Errorf("got %v, want 7", got)
+		}
+	}
+	if stmt.Step() {
+		if got := stmt.ColumnFloat(0); got != 10 {
+			t.Errorf("got %v, want 10", got)
+		}
+	}
+	if stmt.Step() {
+		if got := stmt.ColumnFloat(0); got != 14.5 {
+			t.Errorf("got %v, want 14.5", got)
+		}
+	}
+	if stmt.Step() {
+		if got := stmt.ColumnFloat(0); got != 16 {
+			t.Errorf("got %v, want 16", got)
+		}
+	}
+	stmt.Close()
+
 	stmt, _, err = db.Prepare(`
 		SELECT
 			median(x),