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Statistics: Func-variants of quantile, icdf, percentile, orderstat

v2
Christoph Ruegg 14 years ago
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2 changed files with 147 additions and 0 deletions
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  1. 127
      src/Numerics/Statistics/Statistics.cs
  2. 20
      src/UnitTests/StatisticsTests/StatisticsTests.cs

127
src/Numerics/Statistics/Statistics.cs
View File

@ -258,6 +258,37 @@ namespace MathNet.Numerics.Statistics
return ArrayStatistics.QuantileInplace(array, tau);
}
/// <summary>
/// Estimates the tau-th quantile from the provided samples.
/// The tau-th quantile is the data value where the cumulative distribution
/// function crosses tau.
/// Approximately median-unbiased regardless of the sample distribution (R8).
/// </summary>
/// <param name="data">The data sample sequence.</param>
public static Func<double,double> QuantileFunc(this IEnumerable<double> data)
{
if (data == null) throw new ArgumentNullException("data");
var array = data.ToArray();
Array.Sort(array);
return tau => SortedArrayStatistics.Quantile(array, tau);
}
/// <summary>
/// Estimates the tau-th quantile from the provided samples.
/// The tau-th quantile is the data value where the cumulative distribution
/// function crosses tau.
/// Approximately median-unbiased regardless of the sample distribution (R8).
/// </summary>
/// <param name="data">The data sample sequence.</param>
/// <param name="tau">Quantile selector, between 0.0 and 1.0 (inclusive).</param>
public static Func<double, double> QuantileFunc(this IEnumerable<double?> data)
{
if (data == null) throw new ArgumentNullException("data");
var array = data.Where(d => d.HasValue).Select(d => d.Value).ToArray();
Array.Sort(array);
return tau => SortedArrayStatistics.Quantile(array, tau);
}
/// <summary>
/// Estimates the empiric inverse CDF at tau from the provided samples.
/// </summary>
@ -282,6 +313,30 @@ namespace MathNet.Numerics.Statistics
return ArrayStatistics.QuantileCustomInplace(array, tau, QuantileDefinition.InverseCDF);
}
/// <summary>
/// Estimates the empiric inverse CDF at tau from the provided samples.
/// </summary>
/// <param name="data">The data sample sequence.</param>
public static Func<double, double> InverseCDFFunc(this IEnumerable<double> data)
{
if (data == null) throw new ArgumentNullException("data");
var array = data.ToArray();
Array.Sort(array);
return tau => SortedArrayStatistics.QuantileCustom(array, tau, QuantileDefinition.InverseCDF);
}
/// <summary>
/// Estimates the empiric inverse CDF at tau from the provided samples.
/// </summary>
/// <param name="data">The data sample sequence.</param>
public static Func<double, double> InverseCDFFunc(this IEnumerable<double?> data)
{
if (data == null) throw new ArgumentNullException("data");
var array = data.Where(d => d.HasValue).Select(d => d.Value).ToArray();
Array.Sort(array);
return tau => SortedArrayStatistics.QuantileCustom(array, tau, QuantileDefinition.InverseCDF);
}
/// <summary>
/// stimates the tau-th quantile from the provided samples.
/// The tau-th quantile is the data value where the cumulative distribution
@ -314,6 +369,38 @@ namespace MathNet.Numerics.Statistics
return ArrayStatistics.QuantileCustomInplace(array, tau, definition);
}
/// <summary>
/// stimates the tau-th quantile from the provided samples.
/// The tau-th quantile is the data value where the cumulative distribution
/// function crosses tau. The quantile definition can be specificed to be compatible
/// with an existing system.
/// </summary>
/// <param name="data">The data sample sequence.</param>
/// <param name="definition">Quantile definition, to choose what product/definition it should be consistent with</param>
public static Func<double, double> QuantileCustomFunc(this IEnumerable<double> data, QuantileDefinition definition)
{
if (data == null) throw new ArgumentNullException("data");
var array = data.ToArray();
Array.Sort(array);
return tau => SortedArrayStatistics.QuantileCustom(array, tau, definition);
}
/// <summary>
/// stimates the tau-th quantile from the provided samples.
/// The tau-th quantile is the data value where the cumulative distribution
/// function crosses tau. The quantile definition can be specificed to be compatible
/// with an existing system.
/// </summary>
/// <param name="data">The data sample sequence.</param>
/// <param name="definition">Quantile definition, to choose what product/definition it should be consistent with</param>
public static Func<double, double> QuantileCustomFunc(this IEnumerable<double?> data, QuantileDefinition definition)
{
if (data == null) throw new ArgumentNullException("data");
var array = data.Where(d => d.HasValue).Select(d => d.Value).ToArray();
Array.Sort(array);
return tau => SortedArrayStatistics.QuantileCustom(array, tau, definition);
}
/// <summary>
/// Estimates the p-Percentile value from the provided samples.
/// If a non-integer Percentile is needed, use Quantile instead.
@ -342,6 +429,34 @@ namespace MathNet.Numerics.Statistics
return ArrayStatistics.PercentileInplace(array, p);
}
/// <summary>
/// Estimates the p-Percentile value from the provided samples.
/// If a non-integer Percentile is needed, use Quantile instead.
/// Approximately median-unbiased regardless of the sample distribution (R8).
/// </summary>
/// <param name="data">The data sample sequence.</param>
public static Func<int, double> PercentileFunc(this IEnumerable<double> data)
{
if (data == null) throw new ArgumentNullException("data");
var array = data.ToArray();
Array.Sort(array);
return p => SortedArrayStatistics.Percentile(array, p);
}
/// <summary>
/// Estimates the p-Percentile value from the provided samples.
/// If a non-integer Percentile is needed, use Quantile instead.
/// Approximately median-unbiased regardless of the sample distribution (R8).
/// </summary>
/// <param name="data">The data sample sequence.</param>
public static Func<int, double> PercentileFunc(this IEnumerable<double?> data)
{
if (data == null) throw new ArgumentNullException("data");
var array = data.Where(d => d.HasValue).Select(d => d.Value).ToArray();
Array.Sort(array);
return p => SortedArrayStatistics.Percentile(array, p);
}
/// <summary>
/// Estimates the first quartile value from the provided samples.
/// Approximately median-unbiased regardless of the sample distribution (R8).
@ -449,5 +564,17 @@ namespace MathNet.Numerics.Statistics
var array = data.ToArray();
return ArrayStatistics.OrderStatisticInplace(array, order);
}
/// <summary>
/// Returns the order statistic (order 1..N) from the provided samples.
/// </summary>
/// <param name="data">The data sample sequence.</param>
public static Func<int, double> OrderStatisticFunc(IEnumerable<double> data)
{
if (data == null) throw new ArgumentNullException("data");
var array = data.ToArray();
Array.Sort(array);
return order => SortedArrayStatistics.OrderStatistic(array, order);
}
}
}

20
src/UnitTests/StatisticsTests/StatisticsTests.cs
View File

@ -233,6 +233,16 @@ namespace MathNet.Numerics.UnitTests.StatisticsTests
// -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");
@ -279,7 +289,9 @@ namespace MathNet.Numerics.UnitTests.StatisticsTests
var samples = new[] {-1, 5, 0, -3, 10, -0.5, 4, 0.2, 1, 6};
Assert.AreEqual(expected, Statistics.InverseCDF(samples, tau), 1e-14);
Assert.AreEqual(expected, Statistics.InverseCDFFunc(samples)(tau), 1e-14);
Assert.AreEqual(expected, Statistics.QuantileCustom(samples, tau, QuantileDefinition.InverseCDF), 1e-14);
Assert.AreEqual(expected, Statistics.QuantileCustomFunc(samples, QuantileDefinition.InverseCDF)(tau), 1e-14);
Assert.AreEqual(expected, ArrayStatistics.QuantileCustomInplace(samples, tau, QuantileDefinition.InverseCDF), 1e-14);
Assert.AreEqual(expected, ArrayStatistics.QuantileCustomInplace(samples, tau, 0d, 0d, 1d, 0d), 1e-14);
@ -306,6 +318,7 @@ namespace MathNet.Numerics.UnitTests.StatisticsTests
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);
@ -330,6 +343,7 @@ namespace MathNet.Numerics.UnitTests.StatisticsTests
var samples = new[] {-1, 5, 0, -3, 10, -0.5, 4, 0.2, 1, 6};
Assert.AreEqual(expected, Statistics.QuantileCustom(samples, tau, QuantileDefinition.R3), 1e-14);
Assert.AreEqual(expected, Statistics.QuantileCustomFunc(samples, QuantileDefinition.R3)(tau), 1e-14);
Assert.AreEqual(expected, ArrayStatistics.QuantileCustomInplace(samples, tau, QuantileDefinition.Nearest), 1e-14);
Assert.AreEqual(expected, ArrayStatistics.QuantileCustomInplace(samples, tau, 0.5d, 0d, 0d, 0d), 1e-14);
@ -356,6 +370,7 @@ namespace MathNet.Numerics.UnitTests.StatisticsTests
var samples = new[] {-1, 5, 0, -3, 10, -0.5, 4, 0.2, 1, 6};
Assert.AreEqual(expected, Statistics.QuantileCustom(samples, tau, QuantileDefinition.R4), 1e-14);
Assert.AreEqual(expected, Statistics.QuantileCustomFunc(samples, QuantileDefinition.R4)(tau), 1e-14);
Assert.AreEqual(expected, ArrayStatistics.QuantileCustomInplace(samples, tau, QuantileDefinition.California), 1e-14);
Assert.AreEqual(expected, ArrayStatistics.QuantileCustomInplace(samples, tau, 0d, 0d, 0d, 1d), 1e-14);
@ -382,6 +397,7 @@ namespace MathNet.Numerics.UnitTests.StatisticsTests
var samples = new[] {-1, 5, 0, -3, 10, -0.5, 4, 0.2, 1, 6};
Assert.AreEqual(expected, Statistics.QuantileCustom(samples, tau, QuantileDefinition.R5), 1e-14);
Assert.AreEqual(expected, Statistics.QuantileCustomFunc(samples, QuantileDefinition.R5)(tau), 1e-14);
Assert.AreEqual(expected, ArrayStatistics.QuantileCustomInplace(samples, tau, QuantileDefinition.Hydrology), 1e-14);
Assert.AreEqual(expected, ArrayStatistics.QuantileCustomInplace(samples, tau, 0.5d, 0d, 0d, 1d), 1e-14);
@ -408,6 +424,7 @@ namespace MathNet.Numerics.UnitTests.StatisticsTests
var samples = new[] {-1, 5, 0, -3, 10, -0.5, 4, 0.2, 1, 6};
Assert.AreEqual(expected, Statistics.QuantileCustom(samples, tau, QuantileDefinition.R6), 1e-14);
Assert.AreEqual(expected, Statistics.QuantileCustomFunc(samples, QuantileDefinition.R6)(tau), 1e-14);
Assert.AreEqual(expected, ArrayStatistics.QuantileCustomInplace(samples, tau, QuantileDefinition.Weibull), 1e-14);
Assert.AreEqual(expected, ArrayStatistics.QuantileCustomInplace(samples, tau, 0d, 1d, 0d, 1d), 1e-14);
@ -434,6 +451,7 @@ namespace MathNet.Numerics.UnitTests.StatisticsTests
var samples = new[] {-1, 5, 0, -3, 10, -0.5, 4, 0.2, 1, 6};
Assert.AreEqual(expected, Statistics.QuantileCustom(samples, tau, QuantileDefinition.R7), 1e-14);
Assert.AreEqual(expected, Statistics.QuantileCustomFunc(samples, QuantileDefinition.R7)(tau), 1e-14);
Assert.AreEqual(expected, ArrayStatistics.QuantileCustomInplace(samples, tau, QuantileDefinition.Excel), 1e-14);
Assert.AreEqual(expected, ArrayStatistics.QuantileCustomInplace(samples, tau, 1d, -1d, 0d, 1d), 1e-14);
@ -460,6 +478,7 @@ namespace MathNet.Numerics.UnitTests.StatisticsTests
Assert.AreEqual(expected, Statistics.Quantile(samples, tau), 1e-14);
Assert.AreEqual(expected, Statistics.QuantileCustom(samples, tau, QuantileDefinition.R8), 1e-14);
Assert.AreEqual(expected, Statistics.QuantileCustomFunc(samples, QuantileDefinition.R8)(tau), 1e-14);
Assert.AreEqual(expected, ArrayStatistics.QuantileInplace(samples, tau), 1e-14);
Assert.AreEqual(expected, ArrayStatistics.QuantileCustomInplace(samples, tau, QuantileDefinition.Median), 1e-14);
@ -487,6 +506,7 @@ namespace MathNet.Numerics.UnitTests.StatisticsTests
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);

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