diff --git a/vertical-pod-autoscaler/recommender/util/histogram.go b/vertical-pod-autoscaler/recommender/util/histogram.go
index e41a016f1b..04cf4778eb 100644
--- a/vertical-pod-autoscaler/recommender/util/histogram.go
+++ b/vertical-pod-autoscaler/recommender/util/histogram.go
@@ -33,7 +33,7 @@ type Histogram interface {
 	SubtractSample(value float64, weight float64)
 
 	// Returns true if the histogram is empty.
-	Empty() bool
+	IsEmpty() bool
 }
 
 // NewHistogram returns a new Histogram instance using given options.
@@ -99,7 +99,7 @@ func (h *histogram) SubtractSample(value float64, weight float64) {
 }
 
 func (h *histogram) Percentile(percentile float64) float64 {
-	if h.Empty() {
+	if h.IsEmpty() {
 		return 0.0
 	}
 	partialSum := 0.0
@@ -113,14 +113,15 @@ func (h *histogram) Percentile(percentile float64) float64 {
 	}
 	bucketStart := (*h.options).GetBucketStart(bucket)
 	if bucket < (*h.options).NumBuckets()-1 {
-		// Return the middle of the bucket.
-		nextBucketStart := (*h.options).GetBucketStart(bucket + 1)
-		return (bucketStart + nextBucketStart) / 2.0
+		// Return the middle point between the bucket boundaries.
+		bucketEnd := (*h.options).GetBucketStart(bucket + 1)
+		return (bucketStart + bucketEnd) / 2.0
 	}
-	// For the last bucket return the bucket start.
+	// Return the start of the last bucket (note that the last bucket
+	// doesn't have an upper bound).
 	return bucketStart
 }
 
-func (h *histogram) Empty() bool {
+func (h *histogram) IsEmpty() bool {
 	return h.bucketWeight[h.minBucket] < (*h.options).Epsilon()
 }
diff --git a/vertical-pod-autoscaler/recommender/util/histogram_options.go b/vertical-pod-autoscaler/recommender/util/histogram_options.go
index 7c429656a2..3b1074bc67 100644
--- a/vertical-pod-autoscaler/recommender/util/histogram_options.go
+++ b/vertical-pod-autoscaler/recommender/util/histogram_options.go
@@ -37,14 +37,15 @@ type HistogramOptions interface {
 }
 
 // NewLinearHistogramOptions returns HistogramOptions describing a histogram
-// with a given number of fixed-size buckets, with the first bucket starting
-// at 0.0. Requires maxValue > 0, bucketSize > 0, epsilon > 0.
+// with a given number of fixed-size buckets, with the first bucket start at 0.0
+// and the last bucket start larger or equal to maxValue.
+// Requires maxValue > 0, bucketSize > 0, epsilon > 0.
 func NewLinearHistogramOptions(
 	maxValue float64, bucketSize float64, epsilon float64) (HistogramOptions, error) {
 	if maxValue <= 0.0 || bucketSize <= 0.0 || epsilon <= 0.0 {
 		return nil, errors.New("maxValue and bucketSize must both be positive")
 	}
-	numBuckets := int(math.Ceil(maxValue / bucketSize))
+	numBuckets := int(math.Ceil(maxValue/bucketSize)) + 1
 	return &linearHistogramOptions{numBuckets, bucketSize, epsilon}, nil
 }
 
@@ -52,6 +53,7 @@ func NewLinearHistogramOptions(
 // histogram with exponentially growing bucket boundaries. The first bucket
 // covers the range [0..firstBucketSize). Consecutive buckets are of the form
 // [x(n)..x(n) * ratio) for n = 1 .. numBuckets - 1.
+// The last bucket start is larger or equal to maxValue.
 // Requires maxValue > 0, firstBucketSize > 0, ratio > 1, epsilon > 0.
 func NewExponentialHistogramOptions(
 	maxValue float64, firstBucketSize float64, ratio float64, epsilon float64) (HistogramOptions, error) {
@@ -59,7 +61,7 @@ func NewExponentialHistogramOptions(
 		return nil, errors.New(
 			"maxValue, firstBucketSize and epsilon must be > 0.0, ratio must be > 1.0")
 	}
-	numBuckets := int(math.Ceil(math.Log(maxValue/firstBucketSize)/math.Log(ratio))) + 1
+	numBuckets := int(math.Ceil(math.Log(maxValue/firstBucketSize)/math.Log(ratio))) + 2
 	return &exponentialHistogramOptions{numBuckets, firstBucketSize, ratio, epsilon}, nil
 }
 
diff --git a/vertical-pod-autoscaler/recommender/util/histogram_options_test.go b/vertical-pod-autoscaler/recommender/util/histogram_options_test.go
index 7439823dfa..08e8b6f578 100644
--- a/vertical-pod-autoscaler/recommender/util/histogram_options_test.go
+++ b/vertical-pod-autoscaler/recommender/util/histogram_options_test.go
@@ -31,15 +31,15 @@ func TestLinearHistogramOptions(t *testing.T) {
 	o, err := NewLinearHistogramOptions(5.0, 0.3, epsilon)
 	assert.Nil(t, err)
 	assert.Equal(t, epsilon, o.Epsilon())
-	assert.Equal(t, 17, o.NumBuckets())
+	assert.Equal(t, 18, o.NumBuckets())
 
 	assert.Equal(t, 0.0, o.GetBucketStart(0))
-	assert.Equal(t, 4.8, o.GetBucketStart(16))
+	assert.Equal(t, 5.1, o.GetBucketStart(17))
 
 	assert.Equal(t, 0, o.FindBucket(-1.0))
 	assert.Equal(t, 0, o.FindBucket(0.0))
 	assert.Equal(t, 4, o.FindBucket(1.3))
-	assert.Equal(t, 16, o.FindBucket(100.0))
+	assert.Equal(t, 17, o.FindBucket(100.0))
 }
 
 // Test all methods of ExponentialHistogramOptions using a sample bucketing scheme.
@@ -47,17 +47,18 @@ func TestExponentialHistogramOptions(t *testing.T) {
 	o, err := NewExponentialHistogramOptions(100.0, 10.0, 2.0, epsilon)
 	assert.Nil(t, err)
 	assert.Equal(t, epsilon, o.Epsilon())
-	assert.Equal(t, 5, o.NumBuckets())
+	assert.Equal(t, 6, o.NumBuckets())
 
 	assert.Equal(t, 0.0, o.GetBucketStart(0))
 	assert.Equal(t, 10.0, o.GetBucketStart(1))
 	assert.Equal(t, 20.0, o.GetBucketStart(2))
 	assert.Equal(t, 40.0, o.GetBucketStart(3))
 	assert.Equal(t, 80.0, o.GetBucketStart(4))
+	assert.Equal(t, 160.0, o.GetBucketStart(5))
 
 	assert.Equal(t, 0, o.FindBucket(-1.0))
 	assert.Equal(t, 0, o.FindBucket(9.99))
 	assert.Equal(t, 1, o.FindBucket(10.0))
 	assert.Equal(t, 2, o.FindBucket(20.0))
-	assert.Equal(t, 4, o.FindBucket(100.0))
+	assert.Equal(t, 5, o.FindBucket(200.0))
 }
diff --git a/vertical-pod-autoscaler/recommender/util/histogram_test.go b/vertical-pod-autoscaler/recommender/util/histogram_test.go
index 9182a19099..e515c54d36 100644
--- a/vertical-pod-autoscaler/recommender/util/histogram_test.go
+++ b/vertical-pod-autoscaler/recommender/util/histogram_test.go
@@ -75,19 +75,25 @@ func TestPercentileOutOfBounds(t *testing.T) {
 
 	assert.InEpsilon(t, 0.15, h.Percentile(-0.1), valueEpsilon)
 	assert.InEpsilon(t, 0.25, h.Percentile(1.1), valueEpsilon)
+
+	// Fill the boundary buckets.
+	h.AddSample(0.0, 0.1)
+	h.AddSample(1.0, 0.2)
+	assert.InEpsilon(t, 0.05, h.Percentile(-0.1), valueEpsilon)
+	assert.InEpsilon(t, 1.0, h.Percentile(1.1), valueEpsilon)
 }
 
-// Verifies that Empty() returns true on an empty histogram and false otherwise.
+// Verifies that IsEmpty() returns true on an empty histogram and false otherwise.
 func TestEmptyHistogram(t *testing.T) {
 	options, err := NewLinearHistogramOptions(1.0, 0.1, weightEpsilon)
 	assert.Nil(t, err)
 	h := NewHistogram(options)
 	assert.Nil(t, err)
-	assert.True(t, h.Empty())
+	assert.True(t, h.IsEmpty())
 	h.AddSample(0.1, weightEpsilon*2.5) // Sample weight = epsilon * 2.5.
-	assert.False(t, h.Empty())
+	assert.False(t, h.IsEmpty())
 	h.SubtractSample(0.1, weightEpsilon) // Sample weight = epsilon * 1.5.
-	assert.False(t, h.Empty())
+	assert.False(t, h.IsEmpty())
 	h.SubtractSample(0.1, weightEpsilon) // Sample weight = epsilon * 0.5.
-	assert.True(t, h.Empty())
+	assert.True(t, h.IsEmpty())
 }