public void MedianOnShortSequence()
{
// R: median(c(-1,5,0,-3,10,-0.5,4,0.2,1,6))
// Mathematica: Median[{-1,5,0,-3,10,-1/2,4,1/5,1,6}]
var even = new[] {-1, 5, 0, -3, 10, -0.5, 4, 0.2, 1, 6};
Assert.AreEqual(0.6d, Statistics.Median(even), 1e-14);
Assert.AreEqual(0.6d, ArrayStatistics.MedianInplace(even), 1e-14);
Array.Sort(even);
Assert.AreEqual(0.6d, SortedArrayStatistics.Median(even), 1e-14);
// R: median(c(-1,5,0,-3,10,-0.5,4,0.2,1))
// Mathematica: Median[{-1,5,0,-3,10,-1/2,4,1/5,1}]
var odd = new[] { -1, 5, 0, -3, 10, -0.5, 4, 0.2, 1 };
Assert.AreEqual(0.2d, Statistics.Median(odd), 1e-14);
Assert.AreEqual(0.2d, ArrayStatistics.MedianInplace(odd), 1e-14);
Array.Sort(even);
Assert.AreEqual(0.2d, SortedArrayStatistics.Median(odd), 1e-14);
}
public void QuantileR9NormalOnShortSequence(double tau, double expected)
{
// R: quantile(c(-1,5,0,-3,10,-0.5,4,0.2,1,6),probs=c(0,1,0.5,0.2,0.7,0.01,0.99,0.52,0.325),type=9)
// Mathematica: Quantile[{-1,5,0,-3,10,-1/2,4,1/5,1,6},{0,1,1/2,1/5,7/10,1/100,99/100,13/25,13/40},{{3/8,1/4},{0,1}}]
var samples = new[] {-1, 5, 0, -3, 10, -0.5, 4, 0.2, 1, 6};
Assert.AreEqual(expected, Statistics.QuantileCustom(samples, tau, QuantileDefinition.R9), 1e-14);
Assert.AreEqual(expected, Statistics.QuantileCustomFunc(samples, QuantileDefinition.R9)(tau), 1e-14);
Assert.AreEqual(expected, ArrayStatistics.QuantileCustomInplace(samples, tau, QuantileDefinition.Normal), 1e-14);
Assert.AreEqual(expected, ArrayStatistics.QuantileCustomInplace(samples, tau, 3/8d, 1/4d, 0d, 1d), 1e-14);
Array.Sort(samples);
Assert.AreEqual(expected, SortedArrayStatistics.QuantileCustom(samples, tau, QuantileDefinition.Normal), 1e-14);
Assert.AreEqual(expected, SortedArrayStatistics.QuantileCustom(samples, tau, 3/8d, 1/4d, 0d, 1d), 1e-14);
}
public void OrderStatisticsOnShortSequence()
{
// -3 -1 -0.5 0 1 4 5 6 10
var samples = new[] { -1, 5, 0, -3, 10, -0.5, 4, 1, 6 };
var f = Statistics.OrderStatisticFunc(samples);
Assert.That(f(0), Is.NaN, "Order-0 (bad)");
Assert.That(f(1), Is.EqualTo(-3), "Order-1");
Assert.That(f(2), Is.EqualTo(-1), "Order-2");
Assert.That(f(3), Is.EqualTo(-0.5), "Order-3");
Assert.That(f(7), Is.EqualTo(5), "Order-7");
Assert.That(f(8), Is.EqualTo(6), "Order-8");
Assert.That(f(9), Is.EqualTo(10), "Order-9");
Assert.That(f(10), Is.NaN, "Order-10 (bad)");
Assert.That(Statistics.OrderStatistic(samples, 0), Is.NaN, "Order-0 (bad)");
Assert.That(Statistics.OrderStatistic(samples, 1), Is.EqualTo(-3), "Order-1");
Assert.That(Statistics.OrderStatistic(samples, 2), Is.EqualTo(-1), "Order-2");
Assert.That(Statistics.OrderStatistic(samples, 3), Is.EqualTo(-0.5), "Order-3");
Assert.That(Statistics.OrderStatistic(samples, 7), Is.EqualTo(5), "Order-7");
Assert.That(Statistics.OrderStatistic(samples, 8), Is.EqualTo(6), "Order-8");
Assert.That(Statistics.OrderStatistic(samples, 9), Is.EqualTo(10), "Order-9");
Assert.That(Statistics.OrderStatistic(samples, 10), Is.NaN, "Order-10 (bad)");
Assert.That(ArrayStatistics.OrderStatisticInplace(samples, 0), Is.NaN, "Order-0 (bad)");
Assert.That(ArrayStatistics.OrderStatisticInplace(samples, 1), Is.EqualTo(-3), "Order-1");
Assert.That(ArrayStatistics.OrderStatisticInplace(samples, 2), Is.EqualTo(-1), "Order-2");
Assert.That(ArrayStatistics.OrderStatisticInplace(samples, 3), Is.EqualTo(-0.5), "Order-3");
Assert.That(ArrayStatistics.OrderStatisticInplace(samples, 7), Is.EqualTo(5), "Order-7");
Assert.That(ArrayStatistics.OrderStatisticInplace(samples, 8), Is.EqualTo(6), "Order-8");
Assert.That(ArrayStatistics.OrderStatisticInplace(samples, 9), Is.EqualTo(10), "Order-9");
Assert.That(ArrayStatistics.OrderStatisticInplace(samples, 10), Is.NaN, "Order-10 (bad)");
Array.Sort(samples);
Assert.That(SortedArrayStatistics.OrderStatistic(samples, 0), Is.NaN, "Order-0 (bad)");
Assert.That(SortedArrayStatistics.OrderStatistic(samples, 1), Is.EqualTo(-3), "Order-1");
Assert.That(SortedArrayStatistics.OrderStatistic(samples, 2), Is.EqualTo(-1), "Order-2");
Assert.That(SortedArrayStatistics.OrderStatistic(samples, 3), Is.EqualTo(-0.5), "Order-3");
Assert.That(SortedArrayStatistics.OrderStatistic(samples, 7), Is.EqualTo(5), "Order-7");
Assert.That(SortedArrayStatistics.OrderStatistic(samples, 8), Is.EqualTo(6), "Order-8");
Assert.That(SortedArrayStatistics.OrderStatistic(samples, 9), Is.EqualTo(10), "Order-9");
Assert.That(SortedArrayStatistics.OrderStatistic(samples, 10), Is.NaN, "Order-10 (bad)");
}
public void QuantileR2InverseCDFAverageOnShortSequence(double tau, double expected)
{
// R: quantile(c(-1,5,0,-3,10,-0.5,4,0.2,1,6),probs=c(0,1,0.5,0.2,0.7,0.01,0.99,0.52,0.325),type=2)
// Mathematica: Not Supported
var samples = new[] {-1, 5, 0, -3, 10, -0.5, 4, 0.2, 1, 6};
Assert.AreEqual(expected, Statistics.QuantileCustom(samples, tau, QuantileDefinition.R2), 1e-14);
Assert.AreEqual(expected, Statistics.QuantileCustomFunc(samples, QuantileDefinition.R2)(tau), 1e-14);
Assert.AreEqual(expected, ArrayStatistics.QuantileCustomInplace(samples, tau, QuantileDefinition.InverseCDFAverage), 1e-14);
Array.Sort(samples);
Assert.AreEqual(expected, SortedArrayStatistics.QuantileCustom(samples, tau, QuantileDefinition.InverseCDFAverage), 1e-14);
}
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");
}
