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); }