public void ValidateCumulativeDistribution(double location, double scale, double dof, double x, double p)
{
var dist = new StudentT(location, scale, dof);
Assert.That(dist.CumulativeDistribution(x), Is.EqualTo(p).Within(1e-13));
Assert.That(StudentT.CDF(location, scale, dof, x), Is.EqualTo(p).Within(1e-13));
}
public IList <LinearFitResult> Fit(double[] observations)
{
if (observations.Length != DesignMatrix.RowCount)
{
throw new ArgumentException("Wrong number of rows"); // Not L10N
}
var coefficients = QrFactorization.Solve(observations);
var fittedValues = new double[observations.Length];
var residuals = new double[observations.Length];
for (int iRow = 0; iRow < observations.Length; iRow++)
{
var designRow = Enumerable.Range(0, DesignMatrix.ColumnCount).Select(index => DesignMatrix[iRow, index]).ToArray();
fittedValues[iRow] = DotProduct(designRow, coefficients);
residuals[iRow] = observations[iRow] - fittedValues[iRow];
}
double rss = DotProduct(residuals, residuals);
int degreesOfFreedom = observations.Length - QrFactorization.NumberIndependentColumns;
double resVar = rss / degreesOfFreedom;
double sigma = Math.Sqrt(resVar);
var covarianceUnscaled = MatrixCrossproductInverse;
var scaledCovariance = covarianceUnscaled.Multiply(sigma * sigma);
var indepColIndexes = QrFactorization.IndependentColumnIndexes.ToArray();
var result = new List <LinearFitResult>();
foreach (var contrastRow in ContrastValues.EnumerateRows())
{
double standardError = 0;
for (int iRow = 0; iRow < indepColIndexes.Length; iRow++)
{
for (int iCol = 0; iCol < indepColIndexes.Length; iCol++)
{
standardError += contrastRow[indepColIndexes[iRow]] * scaledCovariance[iRow, iCol] * contrastRow[indepColIndexes[iCol]];
}
}
standardError = Math.Sqrt(standardError);
double foldChange = DotProduct(coefficients, contrastRow);
double tValue = foldChange / standardError;
double pValue;
if (0 != degreesOfFreedom)
{
var studentT = new StudentT(0, 1.0, degreesOfFreedom);
pValue = (1 - studentT.CumulativeDistribution(Math.Abs(tValue))) * 2;
}
else
{
pValue = 1;
}
result.Add(new LinearFitResult(foldChange)
.SetDegreesOfFreedom(degreesOfFreedom)
.SetTValue(tValue)
.SetStandardError(standardError)
.SetPValue(pValue));
}
return(result);
}
public void ValidateCumulativeDistribution(
[Values(0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0)] double location,
[Values(1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0)] double scale,
[Values(1.0, 1.0, 1.0, 1.0, 1.0, 2.0, 2.0, 2.0, 2.0, 2.0, Double.PositiveInfinity, Double.PositiveInfinity, Double.PositiveInfinity)] double dof,
[Values(0.0, 1.0, -1.0, 2.0, -2.0, 0.0, 1.0, -1.0, 2.0, -2.0, 0.0, 1.0, 2.0)] double x,
[Values(0.5, 0.75, 0.25, 0.852416382349567, 0.147583617650433, 0.5, 0.788675134594813, 0.211324865405187, 0.908248290463863, 0.091751709536137, 0.5, 0.841344746068543, 0.977249868051821)] double c)
{
var n = new StudentT(location, scale, dof);
AssertHelpers.AlmostEqual(c, n.CumulativeDistribution(x), 13);
}
public override double Test(IList <double> sample_0, IList <double> sample_1)
{
double mean_1 = ToolsMathStatistics.Mean(sample_0);
double mean_2 = ToolsMathStatistics.Mean(sample_1);
double variance = ToolsMathStatistics.VariancePooled(sample_0, sample_1);
double t_statistic = (mean_1 - mean_2) / (Math.Sqrt(variance) * Math.Sqrt((1.0 / sample_0.Count) + (1.0 / sample_1.Count)));
int degrees_of_freedom = (sample_0.Count + sample_1.Count) - 2;
StudentT distribution = new StudentT(0.1, 1.0, degrees_of_freedom);
return(distribution.CumulativeDistribution(-t_statistic));
}
public static double TestStatic(IList <double> sample_0, IList <double> sample_1)
{
if (sample_0.Count != sample_1.Count)
{
throw new Exception("Samples not of equal size");
}
double[] difference = ToolsMathCollection.SubtractElements(sample_0, sample_1);
double mean_difference = ToolsMathStatistics.Mean(difference);
double variance = ToolsMathStatistics.Variance(difference);
double t_statistic = mean_difference / (Math.Sqrt(variance) / Math.Sqrt(sample_0.Count));
double degrees_of_freedom = (sample_0.Count - 1);
StudentT distribution = new StudentT(0.1, 1.0, degrees_of_freedom);
return(distribution.CumulativeDistribution(t_statistic));
}
public override double Test(IList <double> sample_0, IList <double> sample_1)
{
double mean_0 = ToolsMathStatistics.Mean(sample_0);
double mean_1 = ToolsMathStatistics.Mean(sample_1);
double variance_0 = ToolsMathStatistics.Variance(sample_0, mean_0);
double variance_1 = ToolsMathStatistics.Variance(sample_0, mean_1);
double t_statistic = (mean_0 - mean_1) / Math.Sqrt((variance_0 / sample_0.Count) + (variance_1 / sample_1.Count));
//Welch–Satterthwaite equation:
double dof_nominator = ToolsMath.Sqr((variance_0 / sample_0.Count) + (variance_1 / sample_1.Count));
double dof_denominator =
(Math.Pow(variance_0, 4) / (sample_0.Count * sample_0.Count * (sample_0.Count - 1))) +
(Math.Pow(variance_1, 4) / (sample_1.Count * sample_1.Count * (sample_1.Count - 1)));
double degrees_of_freedom = dof_nominator / dof_denominator;
StudentT distribution = new StudentT(0.1, 1.0, degrees_of_freedom);
return(distribution.CumulativeDistribution(-t_statistic));
}
public void ValidateCumulativeDistribution(double location, double scale, double dof, double x, double c)
{
var n = new StudentT(location, scale, dof);
AssertHelpers.AlmostEqual(c, n.CumulativeDistribution(x), 13);
}
/// <summary>
/// Run example
/// </summary>
/// <a href="http://en.wikipedia.org/wiki/StudentT_distribution">StudentT distribution</a>
public void Run()
{
// 1. Initialize the new instance of the StudentT distribution class with parameters Location = 0, Scale = 1, DegreesOfFreedom = 1
var studentT = new StudentT();
Console.WriteLine(@"1. Initialize the new instance of the StudentT distribution class with parameters Location = {0}, Scale = {1}, DegreesOfFreedom = {2}", studentT.Location, studentT.Scale, studentT.DegreesOfFreedom);
Console.WriteLine();
// 2. Distributuion properties:
Console.WriteLine(@"2. {0} distributuion properties:", studentT);
// Cumulative distribution function
Console.WriteLine(@"{0} - Сumulative distribution at location '0.3'", studentT.CumulativeDistribution(0.3).ToString(" #0.00000;-#0.00000"));
// Probability density
Console.WriteLine(@"{0} - Probability density at location '0.3'", studentT.Density(0.3).ToString(" #0.00000;-#0.00000"));
// Log probability density
Console.WriteLine(@"{0} - Log probability density at location '0.3'", studentT.DensityLn(0.3).ToString(" #0.00000;-#0.00000"));
// Entropy
Console.WriteLine(@"{0} - Entropy", studentT.Entropy.ToString(" #0.00000;-#0.00000"));
// Largest element in the domain
Console.WriteLine(@"{0} - Largest element in the domain", studentT.Maximum.ToString(" #0.00000;-#0.00000"));
// Smallest element in the domain
Console.WriteLine(@"{0} - Smallest element in the domain", studentT.Minimum.ToString(" #0.00000;-#0.00000"));
// Mean
Console.WriteLine(@"{0} - Mean", studentT.Mean.ToString(" #0.00000;-#0.00000"));
// Median
Console.WriteLine(@"{0} - Median", studentT.Median.ToString(" #0.00000;-#0.00000"));
// Mode
Console.WriteLine(@"{0} - Mode", studentT.Mode.ToString(" #0.00000;-#0.00000"));
// Variance
Console.WriteLine(@"{0} - Variance", studentT.Variance.ToString(" #0.00000;-#0.00000"));
// Standard deviation
Console.WriteLine(@"{0} - Standard deviation", studentT.StdDev.ToString(" #0.00000;-#0.00000"));
// 3. Generate 10 samples of the StudentT distribution
Console.WriteLine(@"3. Generate 10 samples of the StudentT distribution");
for (var i = 0; i < 10; i++)
{
Console.Write(studentT.Sample().ToString("N05") + @" ");
}
Console.WriteLine();
Console.WriteLine();
// 4. Generate 100000 samples of the StudentT(0, 1, 1) distribution and display histogram
Console.WriteLine(@"4. Generate 100000 samples of the StudentT(0, 1, 1) distribution and display histogram");
var data = new double[100000];
for (var i = 0; i < data.Length; i++)
{
data[i] = studentT.Sample();
}
ConsoleHelper.DisplayHistogram(data);
// 5. Generate 100000 samples of the StudentT(0, 1, 5) distribution and display histogram
Console.WriteLine(@"5. Generate 100000 samples of the StudentT(0, 1, 5) distribution and display histogram");
studentT.DegreesOfFreedom = 5;
for (var i = 0; i < data.Length; i++)
{
data[i] = studentT.Sample();
}
ConsoleHelper.DisplayHistogram(data);
Console.WriteLine();
// 6. Generate 100000 samples of the StudentT(0, 1, 10) distribution and display histogram
Console.WriteLine(@"6. Generate 100000 samples of the StudentT(0, 1, 10) distribution and display histogram");
studentT.DegreesOfFreedom = 10;
for (var i = 0; i < data.Length; i++)
{
data[i] = studentT.Sample();
}
ConsoleHelper.DisplayHistogram(data);
}
public void ValidateCumulativeDistribution(double location, double scale, double dof, double x, double c)
{
var n = new StudentT(location, scale, dof);
AssertHelpers.AlmostEqual(c, n.CumulativeDistribution(x), 13);
}
public void ValidateCumulativeDistribution(
[Values(0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0)] double location,
[Values(1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0)] double scale,
[Values(1.0, 1.0, 1.0, 1.0, 1.0, 2.0, 2.0, 2.0, 2.0, 2.0, Double.PositiveInfinity, Double.PositiveInfinity, Double.PositiveInfinity)] double dof,
[Values(0.0, 1.0, -1.0, 2.0, -2.0, 0.0, 1.0, -1.0, 2.0, -2.0, 0.0, 1.0, 2.0)] double x,
[Values(0.5, 0.75, 0.25, 0.852416382349567, 0.147583617650433, 0.5, 0.788675134594813, 0.211324865405187, 0.908248290463863, 0.091751709536137, 0.5, 0.841344746068543, 0.977249868051821)] double c)
{
var n = new StudentT(location, scale, dof);
AssertHelpers.AlmostEqual(c, n.CumulativeDistribution(x), 13);
}
public void UpdateP(StudentT tDistribution)
{
this.PValue = 2.0 * tDistribution.CumulativeDistribution(-this.TestStatistics);
}