public void QuantileEstimator_AllEqualTest()
{
double middle = 3.4;
double next = MMath.NextDouble(middle);
double[] x = { middle, middle, middle };
var outer = new OuterQuantiles(x);
Assert.Equal(0.0, outer.GetProbLessThan(middle));
Assert.Equal(middle, outer.GetQuantile(0.0));
Assert.Equal(middle, outer.GetQuantile(0.75));
Assert.Equal(1.0, outer.GetProbLessThan(next));
Assert.Equal(next, outer.GetQuantile(1.0));
foreach (int weight in new[] { 1, 2, 3 })
{
var est = new QuantileEstimator(0.01);
foreach (var item in x)
{
est.Add(item, weight);
}
Assert.Equal(0.0, est.GetProbLessThan(middle));
Assert.Equal(middle, est.GetQuantile(0.0));
Assert.Equal(1.0, est.GetProbLessThan(next));
Assert.Equal(next, est.GetQuantile(1.0));
}
}
public void QuantileEstimator_DoubleDuplicationTest()
{
double first = 1;
double second = 2;
double between = (first + second) / 2;
double next = MMath.NextDouble(second);
double[] x = { first, first, second, second };
// quantiles are 0, 1/3, 2/3, 1
var outer = new OuterQuantiles(x);
Assert.Equal(0.0, outer.GetProbLessThan(first));
Assert.Equal(first, outer.GetQuantile(0.0));
Assert.Equal(0.5, outer.GetProbLessThan(between));
Assert.Equal(between, outer.GetQuantile(0.5));
Assert.Equal(2.0 / 3, outer.GetProbLessThan(second));
Assert.Equal(second, outer.GetQuantile(2.0 / 3));
Assert.Equal(1.0, outer.GetProbLessThan(next));
Assert.Equal(next, outer.GetQuantile(1.0));
CheckGetQuantile(outer, outer);
var inner = InnerQuantiles.FromDistribution(5, outer);
CheckGetQuantile(inner, inner, (int)Math.Ceiling(100.0 / 6), (int)Math.Floor(100.0 * 5 / 6));
var est = new QuantileEstimator(0.01);
est.Add(first, 2);
est.Add(second, 2);
Assert.Equal(0.0, est.GetProbLessThan(first));
Assert.Equal(first, est.GetQuantile(0.0));
Assert.Equal(0.5, est.GetProbLessThan(between));
Assert.Equal(second, est.GetQuantile(2.0 / 3));
Assert.Equal(1.0, est.GetProbLessThan(next));
Assert.Equal(next, est.GetQuantile(1.0));
CheckGetQuantile(est, est);
}
public void QuantileEstimator_DuplicationTest()
{
double middle = 3.4;
double[] x = { 1.2, middle, middle, middle, 5.6 };
var outer = new OuterQuantiles(x);
Assert.Equal(0.25, outer.GetProbLessThan(middle));
Assert.Equal(outer.GetQuantile(0.3), middle);
Assert.Equal(outer.GetQuantile(0.5), middle);
Assert.Equal(outer.GetQuantile(0.7), middle);
CheckGetQuantile(outer, outer);
var inner = InnerQuantiles.FromDistribution(7, outer);
Assert.Equal(0.25, inner.GetProbLessThan(middle));
Assert.Equal(outer.GetQuantile(0.3), middle);
Assert.Equal(outer.GetQuantile(0.5), middle);
Assert.Equal(outer.GetQuantile(0.7), middle);
CheckGetQuantile(inner, inner, (int)Math.Ceiling(100.0 / 8), (int)Math.Floor(100.0 * 7 / 8));
var est = new QuantileEstimator(0.01);
est.AddRange(x);
Assert.Equal(est.GetQuantile(0.3), middle);
Assert.Equal(est.GetQuantile(0.5), middle);
// InterpolationType==1 returns NextDouble(middle)
Assert.Equal(est.GetQuantile(0.7), middle, 1e-15);
CheckGetQuantile(est, est);
}
public void QuantileEstimator_DuplicationTest()
{
double middle = 3.4;
double[] x = { 1.2, middle, middle, middle, 5.6 };
var outer = new OuterQuantiles(x);
Assert.Equal(0.25, outer.GetProbLessThan(middle));
Assert.Equal(outer.GetQuantile(0.3), middle);
Assert.Equal(outer.GetQuantile(0.5), middle);
Assert.Equal(outer.GetQuantile(0.7), middle);
CheckGetQuantile(outer, outer);
var inner = new InnerQuantiles(7, outer);
Assert.Equal(0.25, inner.GetProbLessThan(middle));
Assert.Equal(outer.GetQuantile(0.3), middle);
Assert.Equal(outer.GetQuantile(0.5), middle);
Assert.Equal(outer.GetQuantile(0.7), middle);
CheckGetQuantile(inner, inner, 100 / 8, 100 * 7 / 8);
var est = new QuantileEstimator(0.01);
est.AddRange(x);
Assert.Equal(0.25, est.GetProbLessThan(middle));
Assert.Equal(est.GetQuantile(0.3), middle);
Assert.Equal(est.GetQuantile(0.5), middle);
Assert.Equal(est.GetQuantile(0.7), middle);
CheckGetQuantile(est, est);
}
public void QuantileTest()
{
// draw many samples from N(m,v)
Rand.Restart(0);
int n = 10000;
double m = 2;
double stddev = 3;
Gaussian prior = new Gaussian(m, stddev * stddev);
List <double> x = new List <double>();
for (int i = 0; i < n; i++)
{
x.Add(prior.Sample());
}
x.Sort();
var sortedData = new OuterQuantiles(x.ToArray());
// compute quantiles
var quantiles = InnerQuantiles.FromDistribution(100, sortedData);
// loop over x's and compare true quantile rank
var testPoints = EpTests.linspace(MMath.Min(x) - stddev, MMath.Max(x) + stddev, 100);
double maxError = 0;
foreach (var testPoint in testPoints)
{
var trueRank = MMath.NormalCdf((testPoint - m) / stddev);
var estRank = quantiles.GetProbLessThan(testPoint);
var error = System.Math.Abs(trueRank - estRank);
//Trace.WriteLine($"{testPoint} trueRank={trueRank} estRank={estRank} error={error}");
Assert.True(error < 0.02);
maxError = System.Math.Max(maxError, error);
double estQuantile = quantiles.GetQuantile(estRank);
error = MMath.AbsDiff(estQuantile, testPoint, 1e-8);
//Trace.WriteLine($"{testPoint} estRank={estRank} estQuantile={estQuantile} error={error}");
Assert.True(error < 1e-8);
estRank = sortedData.GetProbLessThan(testPoint);
error = System.Math.Abs(trueRank - estRank);
//Trace.WriteLine($"{testPoint} trueRank={trueRank} estRank={estRank} error={error}");
Assert.True(error < 0.02);
}
//Trace.WriteLine($"max rank error = {maxError}");
}
public void QuantileEstimator_SinglePointIsMedian()
{
QuantileEstimator est = new QuantileEstimator(0.1);
double point = 2;
est.Add(point);
Assert.Equal(point, est.GetQuantile(0.5));
Assert.Equal(0.0, est.GetProbLessThan(point));
OuterQuantiles outer = new OuterQuantiles(new[] { point });
Assert.Equal(point, outer.GetQuantile(0.5));
Assert.Equal(0.0, outer.GetProbLessThan(point));
InnerQuantiles inner = new InnerQuantiles(new[] { point });
Assert.Equal(point, inner.GetQuantile(0.5));
Assert.Equal(0.5, inner.GetProbLessThan(point));
}
private void CheckProbLessThan(CanGetProbLessThan canGetProbLessThan, List <double> x, double maximumError)
{
x.Sort();
var sortedData = new OuterQuantiles(x.ToArray());
// check that quantiles match within the desired accuracy
var min = MMath.Min(x);
var max = MMath.Max(x);
var range = max - min;
var margin = range * 0.01;
var testPoints = EpTests.linspace(min - margin, max + margin, 100);
double maxError = 0;
foreach (var testPoint in testPoints)
{
var trueRank = sortedData.GetProbLessThan(testPoint);
var estRank = canGetProbLessThan.GetProbLessThan(testPoint);
var error = System.Math.Abs(trueRank - estRank);
maxError = System.Math.Max(maxError, error);
}
Console.WriteLine($"max rank error = {maxError}");
Assert.True(maxError <= maximumError);
}
