public void CovarianceConsistentWithVariance(string dataSet)
{
var data = _data[dataSet];
AssertHelpers.AlmostEqualRelative(Statistics.Variance(data.Data), Statistics.Covariance(data.Data, data.Data), 10);
AssertHelpers.AlmostEqualRelative(ArrayStatistics.Variance(data.Data), ArrayStatistics.Covariance(data.Data, data.Data), 10);
AssertHelpers.AlmostEqualRelative(StreamingStatistics.Variance(data.Data), StreamingStatistics.Covariance(data.Data, data.Data), 10);
}
public void PopulationCovarianceConsistentWithPopulationVariance(string dataSet)
{
var data = _data[dataSet];
AssertHelpers.AlmostEqual(Statistics.PopulationVariance(data.Data), Statistics.PopulationCovariance(data.Data, data.Data), 10);
AssertHelpers.AlmostEqual(ArrayStatistics.PopulationVariance(data.Data), ArrayStatistics.PopulationCovariance(data.Data, data.Data), 10);
AssertHelpers.AlmostEqual(StreamingStatistics.PopulationVariance(data.Data), StreamingStatistics.PopulationCovariance(data.Data, data.Data), 10);
}
public void MeanConsistentWithNistData(string dataSet)
{
var data = _data[dataSet];
AssertHelpers.AlmostEqual(data.Mean, Statistics.Mean(data.Data), 15);
AssertHelpers.AlmostEqual(data.Mean, ArrayStatistics.Mean(data.Data), 15);
AssertHelpers.AlmostEqual(data.Mean, StreamingStatistics.Mean(data.Data), 15);
}
public void StandardDeviationConsistentWithNistData(string dataSet, int digits)
{
var data = _data[dataSet];
AssertHelpers.AlmostEqual(data.StandardDeviation, Statistics.StandardDeviation(data.Data), digits);
AssertHelpers.AlmostEqual(data.StandardDeviation, ArrayStatistics.StandardDeviation(data.Data), digits);
AssertHelpers.AlmostEqual(data.StandardDeviation, StreamingStatistics.StandardDeviation(data.Data), digits);
}
public void MeanOfEmptyMustBeNaN()
{
Assert.That(Statistics.Mean(new double[0]), Is.NaN);
Assert.That(Statistics.Mean(new[] { 2d }), Is.Not.NaN);
Assert.That(ArrayStatistics.Mean(new double[0]), Is.NaN);
Assert.That(ArrayStatistics.Mean(new[] { 2d }), Is.Not.NaN);
Assert.That(StreamingStatistics.Mean(new double[0]), Is.NaN);
Assert.That(StreamingStatistics.Mean(new[] { 2d }), Is.Not.NaN);
}
public void ThrowsOnNullData()
{
double[] data = null;
// ReSharper disable InvokeAsExtensionMethod
Assert.That(() => Statistics.Minimum(data), Throws.Exception);
Assert.That(() => Statistics.Maximum(data), Throws.Exception);
Assert.That(() => Statistics.Mean(data), Throws.Exception);
Assert.That(() => Statistics.Median(data), Throws.Exception);
Assert.That(() => Statistics.Quantile(data, 0.3), Throws.Exception);
Assert.That(() => Statistics.Variance(data), Throws.Exception);
Assert.That(() => Statistics.StandardDeviation(data), Throws.Exception);
Assert.That(() => Statistics.PopulationVariance(data), Throws.Exception);
Assert.That(() => Statistics.PopulationStandardDeviation(data), Throws.Exception);
Assert.That(() => Statistics.Covariance(data, data), Throws.Exception);
Assert.That(() => Statistics.PopulationCovariance(data, data), Throws.Exception);
// ReSharper restore InvokeAsExtensionMethod
Assert.That(() => SortedArrayStatistics.Minimum(data), Throws.Exception.TypeOf <NullReferenceException>());
Assert.That(() => SortedArrayStatistics.Minimum(data), Throws.Exception.TypeOf <NullReferenceException>());
Assert.That(() => SortedArrayStatistics.Maximum(data), Throws.Exception.TypeOf <NullReferenceException>());
Assert.That(() => SortedArrayStatistics.OrderStatistic(data, 1), Throws.Exception.TypeOf <NullReferenceException>());
Assert.That(() => SortedArrayStatistics.Median(data), Throws.Exception.TypeOf <NullReferenceException>());
Assert.That(() => SortedArrayStatistics.LowerQuartile(data), Throws.Exception.TypeOf <NullReferenceException>());
Assert.That(() => SortedArrayStatistics.UpperQuartile(data), Throws.Exception.TypeOf <NullReferenceException>());
Assert.That(() => SortedArrayStatistics.Percentile(data, 30), Throws.Exception.TypeOf <NullReferenceException>());
Assert.That(() => SortedArrayStatistics.Quantile(data, 0.3), Throws.Exception.TypeOf <NullReferenceException>());
Assert.That(() => SortedArrayStatistics.QuantileCustom(data, 0.3, 0, 0, 1, 0), Throws.Exception.TypeOf <NullReferenceException>());
Assert.That(() => SortedArrayStatistics.QuantileCustom(data, 0.3, QuantileDefinition.Nearest), Throws.Exception.TypeOf <NullReferenceException>());
Assert.That(() => SortedArrayStatistics.InterquartileRange(data), Throws.Exception.TypeOf <NullReferenceException>());
Assert.That(() => SortedArrayStatistics.FiveNumberSummary(data), Throws.Exception.TypeOf <NullReferenceException>());
Assert.That(() => ArrayStatistics.Minimum(data), Throws.Exception.TypeOf <NullReferenceException>());
Assert.That(() => ArrayStatistics.Maximum(data), Throws.Exception.TypeOf <NullReferenceException>());
Assert.That(() => ArrayStatistics.OrderStatisticInplace(data, 1), Throws.Exception.TypeOf <NullReferenceException>());
Assert.That(() => ArrayStatistics.Mean(data), Throws.Exception.TypeOf <NullReferenceException>());
Assert.That(() => ArrayStatistics.Variance(data), Throws.Exception.TypeOf <NullReferenceException>());
Assert.That(() => ArrayStatistics.StandardDeviation(data), Throws.Exception.TypeOf <NullReferenceException>());
Assert.That(() => ArrayStatistics.PopulationVariance(data), Throws.Exception.TypeOf <NullReferenceException>());
Assert.That(() => ArrayStatistics.PopulationStandardDeviation(data), Throws.Exception.TypeOf <NullReferenceException>());
Assert.That(() => ArrayStatistics.Covariance(data, data), Throws.Exception.TypeOf <NullReferenceException>());
Assert.That(() => ArrayStatistics.PopulationCovariance(data, data), Throws.Exception.TypeOf <NullReferenceException>());
Assert.That(() => ArrayStatistics.MedianInplace(data), Throws.Exception.TypeOf <NullReferenceException>());
Assert.That(() => ArrayStatistics.QuantileInplace(data, 0.3), Throws.Exception.TypeOf <NullReferenceException>());
Assert.That(() => StreamingStatistics.Minimum(data), Throws.Exception.TypeOf <NullReferenceException>());
Assert.That(() => StreamingStatistics.Maximum(data), Throws.Exception.TypeOf <NullReferenceException>());
Assert.That(() => StreamingStatistics.Mean(data), Throws.Exception.TypeOf <NullReferenceException>());
Assert.That(() => StreamingStatistics.Variance(data), Throws.Exception.TypeOf <NullReferenceException>());
Assert.That(() => StreamingStatistics.StandardDeviation(data), Throws.Exception.TypeOf <NullReferenceException>());
Assert.That(() => StreamingStatistics.PopulationVariance(data), Throws.Exception.TypeOf <NullReferenceException>());
Assert.That(() => StreamingStatistics.PopulationStandardDeviation(data), Throws.Exception.TypeOf <NullReferenceException>());
Assert.That(() => StreamingStatistics.Covariance(data, data), Throws.Exception.TypeOf <NullReferenceException>());
Assert.That(() => StreamingStatistics.PopulationCovariance(data, data), Throws.Exception.TypeOf <NullReferenceException>());
}
public void MaximumOfEmptyMustBeNaN()
{
Assert.That(Statistics.Maximum(new double[0]), Is.NaN);
Assert.That(Statistics.Maximum(new[] { 2d }), Is.Not.NaN);
Assert.That(ArrayStatistics.Maximum(new double[0]), Is.NaN);
Assert.That(ArrayStatistics.Maximum(new[] { 2d }), Is.Not.NaN);
Assert.That(SortedArrayStatistics.Maximum(new double[0]), Is.NaN);
Assert.That(SortedArrayStatistics.Maximum(new[] { 2d }), Is.Not.NaN);
Assert.That(StreamingStatistics.Maximum(new double[0]), Is.NaN);
Assert.That(StreamingStatistics.Maximum(new[] { 2d }), Is.Not.NaN);
}
public void StandardDeviationConsistentWithNistData(string dataSet, int digits)
{
var data = _data[dataSet];
AssertHelpers.AlmostEqualRelative(data.StandardDeviation, Statistics.StandardDeviation(data.Data), digits);
AssertHelpers.AlmostEqualRelative(data.StandardDeviation, ArrayStatistics.StandardDeviation(data.Data), digits);
AssertHelpers.AlmostEqualRelative(data.StandardDeviation, StreamingStatistics.StandardDeviation(data.Data), digits);
AssertHelpers.AlmostEqualRelative(data.StandardDeviation, Math.Sqrt(Statistics.MeanVariance(data.Data).Item2), digits);
AssertHelpers.AlmostEqualRelative(data.StandardDeviation, Math.Sqrt(ArrayStatistics.MeanVariance(data.Data).Item2), digits);
AssertHelpers.AlmostEqualRelative(data.StandardDeviation, Math.Sqrt(StreamingStatistics.MeanVariance(data.Data).Item2), digits);
}
public void MeanConsistentWithNistData(string dataSet)
{
var data = _data[dataSet];
AssertHelpers.AlmostEqualRelative(data.Mean, Statistics.Mean(data.Data), 14);
AssertHelpers.AlmostEqualRelative(data.Mean, ArrayStatistics.Mean(data.Data), 14);
AssertHelpers.AlmostEqualRelative(data.Mean, StreamingStatistics.Mean(data.Data), 14);
AssertHelpers.AlmostEqualRelative(data.Mean, Statistics.MeanVariance(data.Data).Item1, 14);
AssertHelpers.AlmostEqualRelative(data.Mean, ArrayStatistics.MeanVariance(data.Data).Item1, 14);
AssertHelpers.AlmostEqualRelative(data.Mean, StreamingStatistics.MeanVariance(data.Data).Item1, 14);
}
public void ArrayStatisticsConsistentWithStreamimgStatistics(string dataSet)
{
var data = _data[dataSet];
AssertHelpers.AlmostEqual(ArrayStatistics.Mean(data.Data), StreamingStatistics.Mean(data.Data), 10);
AssertHelpers.AlmostEqual(ArrayStatistics.Variance(data.Data), StreamingStatistics.Variance(data.Data), 10);
AssertHelpers.AlmostEqual(ArrayStatistics.StandardDeviation(data.Data), StreamingStatistics.StandardDeviation(data.Data), 10);
AssertHelpers.AlmostEqual(ArrayStatistics.PopulationVariance(data.Data), StreamingStatistics.PopulationVariance(data.Data), 10);
AssertHelpers.AlmostEqual(ArrayStatistics.PopulationStandardDeviation(data.Data), StreamingStatistics.PopulationStandardDeviation(data.Data), 10);
AssertHelpers.AlmostEqual(ArrayStatistics.Covariance(data.Data, data.Data), StreamingStatistics.Covariance(data.Data, data.Data), 10);
AssertHelpers.AlmostEqual(ArrayStatistics.PopulationCovariance(data.Data, data.Data), StreamingStatistics.PopulationCovariance(data.Data, data.Data), 10);
}
public void SampleVarianceOfEmptyAndSingleMustBeNaN()
{
Assert.That(Statistics.Variance(new double[0]), Is.NaN);
Assert.That(Statistics.Variance(new[] { 2d }), Is.NaN);
Assert.That(Statistics.Variance(new[] { 2d, 3d }), Is.Not.NaN);
Assert.That(ArrayStatistics.Variance(new double[0]), Is.NaN);
Assert.That(ArrayStatistics.Variance(new[] { 2d }), Is.NaN);
Assert.That(ArrayStatistics.Variance(new[] { 2d, 3d }), Is.Not.NaN);
Assert.That(StreamingStatistics.Variance(new double[0]), Is.NaN);
Assert.That(StreamingStatistics.Variance(new[] { 2d }), Is.NaN);
Assert.That(StreamingStatistics.Variance(new[] { 2d, 3d }), Is.Not.NaN);
}
public void PopulationVarianceOfEmptyMustBeNaN()
{
Assert.That(Statistics.PopulationVariance(new double[0]), Is.NaN);
Assert.That(Statistics.PopulationVariance(new[] { 2d }), Is.Not.NaN);
Assert.That(Statistics.PopulationVariance(new[] { 2d, 3d }), Is.Not.NaN);
Assert.That(ArrayStatistics.PopulationVariance(new double[0]), Is.NaN);
Assert.That(ArrayStatistics.PopulationVariance(new[] { 2d }), Is.Not.NaN);
Assert.That(ArrayStatistics.PopulationVariance(new[] { 2d, 3d }), Is.Not.NaN);
Assert.That(StreamingStatistics.PopulationVariance(new double[0]), Is.NaN);
Assert.That(StreamingStatistics.PopulationVariance(new[] { 2d }), Is.Not.NaN);
Assert.That(StreamingStatistics.PopulationVariance(new[] { 2d, 3d }), Is.Not.NaN);
}
public void ThrowsOnNullData()
{
double[] data = null;
Assert.Throws <ArgumentNullException>(() => Statistics.Minimum(data));
Assert.Throws <ArgumentNullException>(() => Statistics.Maximum(data));
Assert.Throws <ArgumentNullException>(() => Statistics.Mean(data));
Assert.Throws <ArgumentNullException>(() => Statistics.Median(data));
Assert.Throws <ArgumentNullException>(() => Statistics.Quantile(data, 0.3));
Assert.Throws <ArgumentNullException>(() => Statistics.Variance(data));
Assert.Throws <ArgumentNullException>(() => Statistics.StandardDeviation(data));
Assert.Throws <ArgumentNullException>(() => Statistics.PopulationVariance(data));
Assert.Throws <ArgumentNullException>(() => Statistics.PopulationStandardDeviation(data));
Assert.Throws <ArgumentNullException>(() => Statistics.Covariance(data, data));
Assert.Throws <ArgumentNullException>(() => Statistics.PopulationCovariance(data, data));
Assert.Throws <ArgumentNullException>(() => SortedArrayStatistics.Minimum(data));
Assert.Throws <ArgumentNullException>(() => SortedArrayStatistics.Maximum(data));
Assert.Throws <ArgumentNullException>(() => SortedArrayStatistics.OrderStatistic(data, 1));
Assert.Throws <ArgumentNullException>(() => SortedArrayStatistics.Median(data));
Assert.Throws <ArgumentNullException>(() => SortedArrayStatistics.LowerQuartile(data));
Assert.Throws <ArgumentNullException>(() => SortedArrayStatistics.UpperQuartile(data));
Assert.Throws <ArgumentNullException>(() => SortedArrayStatistics.Percentile(data, 30));
Assert.Throws <ArgumentNullException>(() => SortedArrayStatistics.Quantile(data, 0.3));
Assert.Throws <ArgumentNullException>(() => SortedArrayStatistics.QuantileCustom(data, 0.3, 0, 0, 1, 0));
Assert.Throws <ArgumentNullException>(() => SortedArrayStatistics.QuantileCustom(data, 0.3, QuantileDefinition.Nearest));
Assert.Throws <ArgumentNullException>(() => SortedArrayStatistics.InterquartileRange(data));
Assert.Throws <ArgumentNullException>(() => SortedArrayStatistics.FiveNumberSummary(data));
Assert.Throws <ArgumentNullException>(() => ArrayStatistics.Minimum(data));
Assert.Throws <ArgumentNullException>(() => ArrayStatistics.Maximum(data));
Assert.Throws <ArgumentNullException>(() => ArrayStatistics.OrderStatisticInplace(data, 1));
Assert.Throws <ArgumentNullException>(() => ArrayStatistics.Mean(data));
Assert.Throws <ArgumentNullException>(() => ArrayStatistics.Variance(data));
Assert.Throws <ArgumentNullException>(() => ArrayStatistics.StandardDeviation(data));
Assert.Throws <ArgumentNullException>(() => ArrayStatistics.PopulationVariance(data));
Assert.Throws <ArgumentNullException>(() => ArrayStatistics.PopulationStandardDeviation(data));
Assert.Throws <ArgumentNullException>(() => ArrayStatistics.Covariance(data, data));
Assert.Throws <ArgumentNullException>(() => ArrayStatistics.PopulationCovariance(data, data));
Assert.Throws <ArgumentNullException>(() => ArrayStatistics.MedianInplace(data));
Assert.Throws <ArgumentNullException>(() => ArrayStatistics.QuantileInplace(data, 0.3));
Assert.Throws <ArgumentNullException>(() => StreamingStatistics.Minimum(data));
Assert.Throws <ArgumentNullException>(() => StreamingStatistics.Maximum(data));
Assert.Throws <ArgumentNullException>(() => StreamingStatistics.Mean(data));
Assert.Throws <ArgumentNullException>(() => StreamingStatistics.Variance(data));
Assert.Throws <ArgumentNullException>(() => StreamingStatistics.StandardDeviation(data));
Assert.Throws <ArgumentNullException>(() => StreamingStatistics.PopulationVariance(data));
Assert.Throws <ArgumentNullException>(() => StreamingStatistics.PopulationStandardDeviation(data));
Assert.Throws <ArgumentNullException>(() => StreamingStatistics.Covariance(data, data));
Assert.Throws <ArgumentNullException>(() => StreamingStatistics.PopulationCovariance(data, data));
}
public void CovarianceIsSymmetric()
{
var dataA = _data["lottery"].Data.Take(200);
var dataB = _data["lew"].Data.Take(200);
AssertHelpers.AlmostEqual(Statistics.Covariance(dataA, dataB), Statistics.Covariance(dataB, dataA), 12);
AssertHelpers.AlmostEqual(StreamingStatistics.Covariance(dataA, dataB), StreamingStatistics.Covariance(dataB, dataA), 12);
AssertHelpers.AlmostEqual(ArrayStatistics.Covariance(dataA.ToArray(), dataB.ToArray()), ArrayStatistics.Covariance(dataB.ToArray(), dataA.ToArray()), 12);
AssertHelpers.AlmostEqual(Statistics.PopulationCovariance(dataA, dataB), Statistics.PopulationCovariance(dataB, dataA), 12);
AssertHelpers.AlmostEqual(StreamingStatistics.PopulationCovariance(dataA, dataB), StreamingStatistics.PopulationCovariance(dataB, dataA), 12);
AssertHelpers.AlmostEqual(ArrayStatistics.PopulationCovariance(dataA.ToArray(), dataB.ToArray()), ArrayStatistics.PopulationCovariance(dataB.ToArray(), dataA.ToArray()), 12);
}
public void MinimumMaximumOnShortSequence()
{
var samples = new[] { -1.0, 5, 0, -3, 10, -0.5, 4 };
Assert.That(Statistics.Minimum(samples), Is.EqualTo(-3), "Min");
Assert.That(Statistics.Maximum(samples), Is.EqualTo(10), "Max");
Assert.That(ArrayStatistics.Minimum(samples), Is.EqualTo(-3), "Min");
Assert.That(ArrayStatistics.Maximum(samples), Is.EqualTo(10), "Max");
Assert.That(StreamingStatistics.Minimum(samples), Is.EqualTo(-3), "Min");
Assert.That(StreamingStatistics.Maximum(samples), Is.EqualTo(10), "Max");
Array.Sort(samples);
Assert.That(SortedArrayStatistics.Minimum(samples), Is.EqualTo(-3), "Min");
Assert.That(SortedArrayStatistics.Maximum(samples), Is.EqualTo(10), "Max");
}
public void StabilityMeanVariance()
{
// Test around 10^9, potential stability issues
var gaussian = new Normal(1e+9, 2, new MersenneTwister(100));
AssertHelpers.AlmostEqual(1e+9, Statistics.Mean(gaussian.Samples().Take(10000)), 11);
AssertHelpers.AlmostEqual(4d, Statistics.Variance(gaussian.Samples().Take(10000)), 1);
AssertHelpers.AlmostEqual(2d, Statistics.StandardDeviation(gaussian.Samples().Take(10000)), 2);
AssertHelpers.AlmostEqual(1e+9, ArrayStatistics.Mean(gaussian.Samples().Take(10000).ToArray()), 11);
AssertHelpers.AlmostEqual(4d, ArrayStatistics.Variance(gaussian.Samples().Take(10000).ToArray()), 1);
AssertHelpers.AlmostEqual(2d, ArrayStatistics.StandardDeviation(gaussian.Samples().Take(10000).ToArray()), 2);
AssertHelpers.AlmostEqual(1e+9, StreamingStatistics.Mean(gaussian.Samples().Take(10000)), 11);
AssertHelpers.AlmostEqual(4d, StreamingStatistics.Variance(gaussian.Samples().Take(10000)), 1);
AssertHelpers.AlmostEqual(2d, StreamingStatistics.StandardDeviation(gaussian.Samples().Take(10000)), 2);
}
public void DoesNotThrowOnEmptyData()
{
double[] data = new double[0];
Assert.DoesNotThrow(() => Statistics.Minimum(data));
Assert.DoesNotThrow(() => Statistics.Maximum(data));
Assert.DoesNotThrow(() => Statistics.Mean(data));
Assert.DoesNotThrow(() => Statistics.Median(data));
Assert.DoesNotThrow(() => Statistics.Quantile(data, 0.3));
Assert.DoesNotThrow(() => Statistics.Variance(data));
Assert.DoesNotThrow(() => Statistics.StandardDeviation(data));
Assert.DoesNotThrow(() => Statistics.PopulationVariance(data));
Assert.DoesNotThrow(() => Statistics.PopulationStandardDeviation(data));
Assert.DoesNotThrow(() => SortedArrayStatistics.Minimum(data));
Assert.DoesNotThrow(() => SortedArrayStatistics.Maximum(data));
Assert.DoesNotThrow(() => SortedArrayStatistics.OrderStatistic(data, 1));
Assert.DoesNotThrow(() => SortedArrayStatistics.Median(data));
Assert.DoesNotThrow(() => SortedArrayStatistics.LowerQuartile(data));
Assert.DoesNotThrow(() => SortedArrayStatistics.UpperQuartile(data));
Assert.DoesNotThrow(() => SortedArrayStatistics.Percentile(data, 30));
Assert.DoesNotThrow(() => SortedArrayStatistics.Quantile(data, 0.3));
Assert.DoesNotThrow(() => SortedArrayStatistics.QuantileCustom(data, 0.3, 0, 0, 1, 0));
Assert.DoesNotThrow(() => SortedArrayStatistics.QuantileCustom(data, 0.3, QuantileDefinition.Nearest));
Assert.DoesNotThrow(() => SortedArrayStatistics.InterquartileRange(data));
Assert.DoesNotThrow(() => SortedArrayStatistics.FiveNumberSummary(data));
Assert.DoesNotThrow(() => ArrayStatistics.Minimum(data));
Assert.DoesNotThrow(() => ArrayStatistics.Maximum(data));
Assert.DoesNotThrow(() => ArrayStatistics.OrderStatisticInplace(data, 1));
Assert.DoesNotThrow(() => ArrayStatistics.Mean(data));
Assert.DoesNotThrow(() => ArrayStatistics.Variance(data));
Assert.DoesNotThrow(() => ArrayStatistics.StandardDeviation(data));
Assert.DoesNotThrow(() => ArrayStatistics.PopulationVariance(data));
Assert.DoesNotThrow(() => ArrayStatistics.PopulationStandardDeviation(data));
Assert.DoesNotThrow(() => ArrayStatistics.MedianInplace(data));
Assert.DoesNotThrow(() => ArrayStatistics.QuantileInplace(data, 0.3));
Assert.DoesNotThrow(() => StreamingStatistics.Minimum(data));
Assert.DoesNotThrow(() => StreamingStatistics.Maximum(data));
Assert.DoesNotThrow(() => StreamingStatistics.Mean(data));
Assert.DoesNotThrow(() => StreamingStatistics.Variance(data));
Assert.DoesNotThrow(() => StreamingStatistics.StandardDeviation(data));
Assert.DoesNotThrow(() => StreamingStatistics.PopulationVariance(data));
Assert.DoesNotThrow(() => StreamingStatistics.PopulationStandardDeviation(data));
}
