public void InverseDistributionFunctionTest()
{
TDistribution target;
double[] expected;
target = new TDistribution(1);
expected = new double[] { 6.3138, 3.0777, 1.9626, 1.3764, 1, 0.7265, 0.5095, 0.3249, 0.1584, 0 };
for (int i = 1; i <= 10; i++)
{
double percent = i / 10.0;
double actual = target.InverseDistributionFunction(1.0 - percent / 2);
Assert.AreEqual(expected[i - 1], actual, 1e-4);
Assert.IsFalse(Double.IsNaN(actual));
}
target = new TDistribution(4.2);
expected = new double[] { 2.103, 1.5192, 1.1814, 0.9358, 0.7373, 0.5664, 0.4127, 0.2699, 0.1334, 0 };
for (int i = 1; i <= 10; i++)
{
double percent = i / 10.0;
double actual = target.InverseDistributionFunction(1.0 - percent / 2);
Assert.AreEqual(expected[i - 1], actual, 1e-4);
Assert.IsFalse(Double.IsNaN(actual));
}
}
protected override void EndProcessing()
{
var dist = new TDistribution(DegreesOfFreedom);
var obj = DistributionHelper.AddConvinienceMethods(dist);
WriteObject(obj);
}
public void ProbabilityDensityFunctionTest()
{
TDistribution target = new TDistribution(1);
double expected = 0.31830988618379075;
double actual = target.ProbabilityDensityFunction(0);
Assert.AreEqual(expected, actual);
expected = 0.017076710632177614;
actual = target.ProbabilityDensityFunction(4.2);
Assert.AreEqual(expected, actual);
target = new TDistribution(2);
expected = 0.35355339059327379;
actual = target.ProbabilityDensityFunction(0);
Assert.AreEqual(expected, actual);
expected = 0.011489146700777093;
actual = target.ProbabilityDensityFunction(4.2);
Assert.AreEqual(expected, actual);
target = new TDistribution(3);
expected = 0.36755259694786141;
actual = target.ProbabilityDensityFunction(0);
Assert.AreEqual(expected, actual);
expected = 0.0077650207237835792;
actual = target.ProbabilityDensityFunction(4.2);
Assert.AreEqual(expected, actual);
}
public void ConstructorTest()
{
var t = new TDistribution(degreesOfFreedom: 4.2);
double mean = t.Mean; // 0.0
double median = t.Median; // 0.0
double var = t.Variance; // 1.9090909090909089
double cdf = t.DistributionFunction(x: 1.4); // 0.88456136730659074
double pdf = t.ProbabilityDensityFunction(x: 1.4); // 0.13894002185341031
double lpdf = t.LogProbabilityDensityFunction(x: 1.4); // -1.9737129364307417
double ccdf = t.ComplementaryDistributionFunction(x: 1.4); // 0.11543863269340926
double icdf = t.InverseDistributionFunction(p: cdf); // 1.4000000000000012
double hf = t.HazardFunction(x: 1.4); // 1.2035833984833988
double chf = t.CumulativeHazardFunction(x: 1.4); // 2.1590162088918525
string str = t.ToString(CultureInfo.InvariantCulture); // T(x; df = 4.2)
Assert.AreEqual(0.0, mean);
Assert.AreEqual(0.0, median);
Assert.AreEqual(1.9090909090909089, var);
Assert.AreEqual(2.1590162088918525, chf);
Assert.AreEqual(0.88456136730659074, cdf);
Assert.AreEqual(0.13894002185341031, pdf);
Assert.AreEqual(-1.9737129364307417, lpdf);
Assert.AreEqual(1.2035833984833988, hf);
Assert.AreEqual(0.11543863269340926, ccdf);
Assert.AreEqual(1.4000000000000012, icdf);
Assert.AreEqual("T(x; df = 4.2)", str);
}
public ActionResult Contrast(FormCollection form)
{
ViewBag.SSA = form.GetValues("ssa").Select(x => double.Parse(x)).FirstOrDefault();
ViewBag.SSE = form.GetValues("sse").Select(x => double.Parse(x)).FirstOrDefault();
ViewBag.Ftest = form.GetValues("ftest").Select(x => double.Parse(x)).FirstOrDefault();
ViewBag.Sc = form.GetValues("Sc").Select(x => double.Parse(x)).FirstOrDefault();
ViewBag.n = form.GetValues("n").Select(x => int.Parse(x)).FirstOrDefault();
ViewBag.k = form.GetValues("k").Select(x => int.Parse(x)).FirstOrDefault();
ViewBag.Alt1 = form.GetValues("alt1").Select(x => int.Parse(x)).FirstOrDefault();
ViewBag.Alt2 = form.GetValues("alt2").Select(x => int.Parse(x)).FirstOrDefault();
ViewBag.Certainty = form.GetValues("certainty").Select(x => double.Parse(x)).FirstOrDefault();
string alts = form.GetValues("alts").FirstOrDefault();
ViewBag.alts = alts.Split(',').Select(x => double.Parse(x)).ToArray();
double c = ViewBag.alts[ViewBag.Alt1 - 1] - ViewBag.alts[ViewBag.Alt2 - 1];
var tdist = new TDistribution(ViewBag.k * (ViewBag.n - 1));
double alpha = 1 - ViewBag.Certainty;
double div = tdist.InverseCDF(1 - alpha / 2) * ViewBag.Sc;
ViewBag.LowLimit = c - div;
ViewBag.HighLimit = c + div;
return(View("Result"));
}
public void LogProbabilityDensityFunctionTest()
{
TDistribution target = new TDistribution(1);
double expected = System.Math.Log(0.31830988618379075);
double actual = target.LogProbabilityDensityFunction(0);
Assert.AreEqual(expected, actual);
expected = System.Math.Log(0.017076710632177614);
actual = target.LogProbabilityDensityFunction(4.2);
Assert.AreEqual(expected, actual, 1e-6);
target = new TDistribution(2);
expected = System.Math.Log(0.35355339059327379);
actual = target.LogProbabilityDensityFunction(0);
Assert.AreEqual(expected, actual, 1e-6);
expected = System.Math.Log(0.011489146700777093);
actual = target.LogProbabilityDensityFunction(4.2);
Assert.AreEqual(expected, actual, 1e-6);
target = new TDistribution(3);
expected = System.Math.Log(0.36755259694786141);
actual = target.LogProbabilityDensityFunction(0);
Assert.AreEqual(expected, actual, 1e-6);
expected = System.Math.Log(0.0077650207237835792);
actual = target.LogProbabilityDensityFunction(4.2);
Assert.AreEqual(expected, actual, 1e-6);
}
/// <summary>
/// Tests the null hypothesis that the population mean is equal to a specified value.
/// </summary>
///
public TTest(double[] sample, double hypothesizedMean, TTestHypotesis type)
{
int n = sample.Length;
double x = Accord.Statistics.Tools.Mean(sample);
double s = Accord.Statistics.Tools.StandardDeviation(sample, x);
StatisticDistribution = new TDistribution(n - 1);
Statistic = (x - hypothesizedMean) / (s / Math.Sqrt(n));
if (type == TTestHypotesis.MeanIsDifferentThanHypothesis)
{
PValue = 2.0 * StatisticDistribution.SurvivalFunction(Statistic);
Hypothesis = Testing.Hypothesis.TwoTail;
}
else if (type == TTestHypotesis.MeanIsGreaterThanHypothesis)
{
PValue = StatisticDistribution.SurvivalFunction(Statistic);
Hypothesis = Testing.Hypothesis.OneUpper;
}
else if (type == TTestHypotesis.MeanIsSmallerThanHypothesis)
{
PValue = StatisticDistribution.DistributionFunction(Statistic);
Hypothesis = Testing.Hypothesis.OneLower;
}
}
public void TestCriticalPointCalculation()
{
foreach (int key in s_T_Coeff_95.Keys)
{
var coeff = TDistribution.CalculateCriticalValue(key, (1 - 0.95), 0.0001);
Assert.AreEqual(s_T_Coeff_95[key], coeff, 0.002);
}
}
public void FitTest()
{
bool thrown = false;
TDistribution target = new TDistribution(1);
try { target.Fit(null, null, null); }
catch (NotSupportedException) { thrown = true; }
Assert.IsTrue(thrown);
}
public void InverseDistributionFunctionTest2()
{
TDistribution target = new TDistribution(24);
double expected = 1.710882023;
double actual = target.InverseDistributionFunction(0.95);
Assert.AreEqual(expected, actual, 1e-06);
}
public double GetSignificance()
{
if (this.n < 3L)
{
return(Double.NaN);
}
TDistribution distribution = new TDistribution(this.n - 2L);
return(2.0D * (1.0D - distribution.cumulativeProbability(Math.Abs(GetSlope()) / GetSlopeStdErr())));
}
public void CloneTest()
{
int degreesOfFreedom = 5;
TDistribution target = new TDistribution(degreesOfFreedom);
TDistribution clone = (TDistribution)target.Clone();
Assert.AreNotSame(target, clone);
Assert.AreEqual(target.DegreesOfFreedom, clone.DegreesOfFreedom);
Assert.AreEqual(target.Mean, clone.Mean);
Assert.AreEqual(target.Variance, clone.Variance);
}
public void ConstructorTest()
{
var t = new TDistribution(degreesOfFreedom: 4.2);
double mean = t.Mean; // 0.0
double median = t.Median; // 0.0
double var = t.Variance; // 1.9090909090909089
double mode = t.Mode;
double cdf = t.DistributionFunction(x: 1.4); // 0.88456136730659074
double pdf = t.ProbabilityDensityFunction(x: 1.4); // 0.13894002185341031
double lpdf = t.LogProbabilityDensityFunction(x: 1.4); // -1.9737129364307417
double ccdf = t.ComplementaryDistributionFunction(x: 1.4); // 0.11543863269340926
double icdf = t.InverseDistributionFunction(p: cdf); // 1.4000000000000012
double hf = t.HazardFunction(x: 1.4); // 1.2035833984833988
double chf = t.CumulativeHazardFunction(x: 1.4); // 2.1590162088918525
string str = t.ToString(CultureInfo.InvariantCulture); // T(x; df = 4.2)
Assert.AreEqual(double.NegativeInfinity, t.Support.Min);
Assert.AreEqual(double.PositiveInfinity, t.Support.Max);
double icdf0 = t.InverseDistributionFunction(0);
double icdf1 = t.InverseDistributionFunction(1);
Assert.AreEqual(icdf0, t.Support.Min);
Assert.AreEqual(icdf1, t.Support.Max);
Assert.AreEqual(0.0, mean);
Assert.AreEqual(0.0, median);
Assert.AreEqual(0.0, mode);
Assert.AreEqual(1.9090909090909089, var);
Assert.AreEqual(2.1590162088918525, chf);
Assert.AreEqual(0.88456136730659074, cdf);
Assert.AreEqual(0.13894002185341031, pdf);
Assert.AreEqual(-1.9737129364307417, lpdf);
Assert.AreEqual(1.2035833984833988, hf);
Assert.AreEqual(0.11543863269340926, ccdf);
Assert.AreEqual(1.4000000000000012, icdf);
Assert.AreEqual("T(x; df = 4.2)", str);
var range1 = t.GetRange(0.95);
var range2 = t.GetRange(0.99);
var range3 = t.GetRange(0.01);
Assert.AreEqual(-2.1030107450099362, range1.Min);
Assert.AreEqual(2.1030107450099362, range1.Max);
Assert.AreEqual(-3.6502571302187774, range2.Min);
Assert.AreEqual(3.6502571302187774, range2.Max);
Assert.AreEqual(-3.6502571302187792, range3.Min);
Assert.AreEqual(3.6502571302187774, range3.Max);
}
public StudentUniformDistribution(double uniformLowerBound, double uniformUpperBound, double mean, double tStd, double degreesOfFreedom)
{
ua = uniformLowerBound;
ub = uniformUpperBound;
df = degreesOfFreedom;
tm = mean;
ts = tStd;
baseDistribution = new TDistribution(df);
this.mean = ((ua + ub) / 2d) + tm;
variance = (Math.Pow(ts, 2) * df / (df - 2)) + (Math.Pow(ub - ua, 2) / 12d);
}
/// <summary>
/// confidence level is alpha
/// </summary>
/// <param name="alpha"></param>
/// <returns></returns>
public ClosedNeighborhood <double> meanDifferenceConfidenceInterval(int levelA, int levelB, double confidenceLevel)
{
return(new ClosedNeighborhood <double>(
observationsAverageByLevel(levelA) - observationsAverageByLevel(levelB),
TDistribution.UpperDividePoint((1 - confidenceLevel) / 2, this.degreesOfFreedomError)
*
((errorSquareAverage
* (1.0 / observationsCountByLevel(levelA) + 1.0 / observationsCountByLevel(levelB))
).Power(.5))
));
}
public void InverseDistributionFunctionLeftTailTest()
{
double[] a = { 0.1, 0.05, 0.025, 0.01, 0.005, 0.001, 0.0005 };
double[,] expected =
{
{ 1, 3.078, 6.314, 12.706, 31.821, 63.656, 318.289, 636.578 },
{ 2, 1.886, 2.920, 4.303, 6.965, 9.925, 22.328, 31.600 },
{ 3, 1.638, 2.353, 3.182, 4.541, 5.841, 10.214, 12.924 },
{ 4, 1.533, 2.132, 2.776, 3.747, 4.604, 7.173, 8.610 },
{ 5, 1.476, 2.015, 2.571, 3.365, 4.032, 5.894, 6.869 },
{ 6, 1.440, 1.943, 2.447, 3.143, 3.707, 5.208, 5.959 },
{ 7, 1.415, 1.895, 2.365, 2.998, 3.499, 4.785, 5.408 },
{ 8, 1.397, 1.860, 2.306, 2.896, 3.355, 4.501, 5.041 },
{ 9, 1.383, 1.833, 2.262, 2.821, 3.250, 4.297, 4.781 },
{ 10, 1.372, 1.812, 2.228, 2.764, 3.169, 4.144, 4.587 },
{ 11, 1.363, 1.796, 2.201, 2.718, 3.106, 4.025, 4.437 },
{ 12, 1.356, 1.782, 2.179, 2.681, 3.055, 3.930, 4.318 },
{ 13, 1.350, 1.771, 2.160, 2.650, 3.012, 3.852, 4.221 },
{ 14, 1.345, 1.761, 2.145, 2.624, 2.977, 3.787, 4.140 },
{ 15, 1.341, 1.753, 2.131, 2.602, 2.947, 3.733, 4.073 },
{ 16, 1.337, 1.746, 2.120, 2.583, 2.921, 3.686, 4.015 },
{ 17, 1.333, 1.740, 2.110, 2.567, 2.898, 3.646, 3.965 },
{ 18, 1.330, 1.734, 2.101, 2.552, 2.878, 3.610, 3.922 },
{ 19, 1.328, 1.729, 2.093, 2.539, 2.861, 3.579, 3.883 },
{ 20, 1.325, 1.725, 2.086, 2.528, 2.845, 3.552, 3.850 },
{ 21, 1.323, 1.721, 2.080, 2.518, 2.831, 3.527, 3.819 },
{ 22, 1.321, 1.717, 2.074, 2.508, 2.819, 3.505, 3.792 },
{ 23, 1.319, 1.714, 2.069, 2.500, 2.807, 3.485, 3.768 },
{ 24, 1.318, 1.711, 2.064, 2.492, 2.797, 3.467, 3.745 },
{ 25, 1.316, 1.708, 2.060, 2.485, 2.787, 3.450, 3.725 },
{ 26, 1.315, 1.706, 2.056, 2.479, 2.779, 3.435, 3.707 },
{ 27, 1.314, 1.703, 2.052, 2.473, 2.771, 3.421, 3.689 },
{ 28, 1.313, 1.701, 2.048, 2.467, 2.763, 3.408, 3.674 },
{ 29, 1.311, 1.699, 2.045, 2.462, 2.756, 3.396, 3.660 },
{ 30, 1.310, 1.697, 2.042, 2.457, 2.750, 3.385, 3.646 },
{ 60, 1.296, 1.671, 2.000, 2.390, 2.660, 3.232, 3.460 },
{ 120, 1.289, 1.658, 1.980, 2.358, 2.617, 3.160, 3.373 },
};
for (int i = 0; i < expected.GetLength(0); i++)
{
int df = (int)expected[i, 0];
TDistribution target = new TDistribution(df);
for (int j = 1; j < expected.GetLength(1); j++)
{
double actual = target.InverseDistributionFunction(1.0 - a[j - 1]);
Assert.IsTrue(Math.Abs(expected[i, j] / actual - 1) < 1e-3);
}
}
}
public StudentUniformDistribution(double n, double degreesOfFreedom)
{
ts = Math.Sqrt(1d / (Math.Pow(n, 2) + 1d));
double a = n * ts * Math.Sqrt(3);
df = degreesOfFreedom;
ua = -a;
ub = a;
tm = 0;
baseDistribution = new TDistribution(df);
mean = 0;
variance = (Math.Pow(ts, 2) * df / (df - 2)) + (Math.Pow(a, 2) / 3d);
}
public double GetSlopeConfidenceInterval(double alpha)
{
if (this.n < 3L)
{
return(Double.NaN);
}
if ((alpha >= 1.0D) || (alpha <= 0.0D))
{
// throw new OutOfRangeException(LocalizedFormats.SIGNIFICANCE_LEVEL, Double.valueOf(alpha), Integer.valueOf(0), Integer.valueOf(1));
}
TDistribution distribution = new TDistribution(this.n - 2L);
return(GetSlopeStdErr() * distribution.inverseCumulativeProbability(1.0D - alpha / 2.0D));
}
public void VarianceTest()
{
TDistribution target = new TDistribution(3);
double actual = target.Variance;
double expected = 3;
Assert.AreEqual(expected, actual);
target = new TDistribution(2);
actual = target.Variance;
expected = Double.PositiveInfinity;
Assert.AreEqual(expected, actual);
target = new TDistribution(1);
actual = target.Variance;
Assert.IsTrue(Double.IsNaN(actual));
}
public void TDistributionConstructorTest()
{
int degreesOfFreedom = 4;
TDistribution target = new TDistribution(degreesOfFreedom);
Assert.AreEqual(degreesOfFreedom, target.DegreesOfFreedom);
bool thrown = false;
try { target = new TDistribution(0); }
catch (ArgumentOutOfRangeException) { thrown = true; }
Assert.IsTrue(thrown);
thrown = false;
try { target = new TDistribution(-1); }
catch (ArgumentOutOfRangeException) { thrown = true; }
Assert.IsTrue(thrown);
}
public StudentGeneralizedDistribution(double mean, double std, double degreesOfFreedom)
{
ScaleCoefficient = std;
this.mean = mean;
DegreesOfFreedom = degreesOfFreedom;
baseT = new TDistribution(degreesOfFreedom);
baseNormal = new NormalDistribution(0, 1);
gammaDistr = new GammaDistribution(2.0, 0.5 * degreesOfFreedom);
if (degreesOfFreedom > 2)
{
variance = Math.Pow(ScaleCoefficient, 2) * degreesOfFreedom / (degreesOfFreedom - 2);
}
else
{
variance = double.NaN;
}
}
public void MeanTest()
{
TDistribution target;
double actual;
target = new TDistribution(1);
actual = target.Mean;
Assert.IsTrue(Double.IsNaN(actual));
target = new TDistribution(2);
actual = target.Mean;
double expected = 0;
Assert.AreEqual(expected, actual);
target = new TDistribution(3);
actual = target.Mean;
expected = 0;
Assert.AreEqual(expected, actual);
}
private LeastSquaresRegressionResult getResultWithStatistics(double[][] x, double[] y, double[] betas, double[] yModel, DoubleMatrix transpose, DoubleMatrix matrix, bool useIntercept)
{
double yMean = 0.0;
foreach (double y1 in y)
{
yMean += y1;
}
yMean /= y.Length;
double totalSumOfSquares = 0.0;
double errorSumOfSquares = 0.0;
int n = x.Length;
int k = betas.Length;
double[] residuals = new double[n];
double[] stdErrorBetas = new double[k];
double[] tStats = new double[k];
double[] pValues = new double[k];
for (int i = 0; i < n; i++)
{
totalSumOfSquares += (y[i] - yMean) * (y[i] - yMean);
residuals[i] = y[i] - yModel[i];
errorSumOfSquares += residuals[i] * residuals[i];
}
double regressionSumOfSquares = totalSumOfSquares - errorSumOfSquares;
double[][] covarianceBetas = convertArray(_algebra.getInverse(_algebra.multiply(transpose, matrix)).toArray());
double rSquared = regressionSumOfSquares / totalSumOfSquares;
double adjustedRSquared = 1.0 - (1 - rSquared) * (n - 1.0) / (n - k);
double meanSquareError = errorSumOfSquares / (n - k);
TDistribution studentT = new TDistribution(n - k);
for (int i = 0; i < k; i++)
{
stdErrorBetas[i] = Math.Sqrt(meanSquareError * covarianceBetas[i][i]);
tStats[i] = betas[i] / stdErrorBetas[i];
pValues[i] = 1 - studentT.cumulativeProbability(Math.Abs(tStats[i]));
}
return(new LeastSquaresRegressionResult(betas, residuals, meanSquareError, stdErrorBetas, rSquared, adjustedRSquared, tStats, pValues, useIntercept));
}
/// <summary>
/// Computes the power for a test with givens values of
/// <see cref="IPowerAnalysis.Effect">effect size</see> and <see cref="IPowerAnalysis.Samples">
/// number of samples</see> under <see cref="IPowerAnalysis.Size"/>.
/// </summary>
///
/// <returns>
/// The power for the test under the given conditions.
/// </returns>
///
public override void ComputePower()
{
double delta = Effect / Math.Sqrt(1.0 / Samples1 + 1.0 / Samples2);
double df = Samples1 + Samples2 - 2;
TDistribution td = new TDistribution(df);
NoncentralTDistribution nt = new NoncentralTDistribution(df, delta);
switch (Tail)
{
case DistributionTail.TwoTail:
{
double Ta = td.InverseDistributionFunction(1.0 - Size / 2);
double pa = nt.ComplementaryDistributionFunction(+Ta);
double pb = nt.DistributionFunction(-Ta);
Power = pa + pb;
break;
}
case DistributionTail.OneLower:
{
double Ta = td.InverseDistributionFunction(Size);
Power = nt.DistributionFunction(Ta);
break;
}
case DistributionTail.OneUpper:
{
double Ta = td.InverseDistributionFunction(1.0 - Size);
Power = nt.ComplementaryDistributionFunction(Ta);
break;
}
default:
throw new InvalidOperationException();
}
}
public void DistributionFunctionTest()
{
TDistribution target = new TDistribution(1);
double expected = 0.5;
double actual = target.DistributionFunction(0);
Assert.IsFalse(Double.IsNaN(actual));
Assert.AreEqual(expected, actual, 1e-15);
expected = 0.92559723470138278;
actual = target.DistributionFunction(4.2);
Assert.AreEqual(expected, actual);
target = new TDistribution(2);
expected = 0.5;
actual = target.DistributionFunction(0);
Assert.AreEqual(expected, actual);
expected = 0.97385836652685043;
actual = target.DistributionFunction(4.2);
Assert.AreEqual(expected, actual);
target = new TDistribution(3);
expected = 0.5;
actual = target.DistributionFunction(0);
Assert.IsFalse(Double.IsNaN(actual));
Assert.AreEqual(expected, actual, 1e-15);
expected = 0.98768396091153043;
actual = target.DistributionFunction(4.2);
Assert.AreEqual(expected, actual);
expected = 0.16324737815131229;
actual = target.DistributionFunction(-1.17);
Assert.AreEqual(expected, actual);
}
public RealMatrix GetCorrelationPValues()
{
TDistribution tDistribution = new TDistribution(this.nObs - 2);
int nVars = this.correlationMatrix.getColumnDimension();
double[][] outVar = new double[nVars][];
for (int i = 0; i < nVars; i++)
{
for (int j = 0; j < nVars; j++)
{
if (i == j)
{
outVar[i][j] = 0.0D;
}
else
{
double r = this.correlationMatrix.getEntry(i, j);
double t = Math.Abs(r * Math.Sqrt((this.nObs - 2) / (1.0D - r * r)));
outVar[i][j] = (2.0D * tDistribution.cumulativeProbability(-t));
}
}
}
return(new BlockRealMatrix(outVar));
}
/// <summary>
/// H0:b=0.
/// If b=0 is rejected, the linear is conspicuous.
/// </summary>
public ISet <IReal> conspicuousDomain(double alpha)
{
return
((ISet <IReal>)
(
(new IntervalLeftOpenRightInfinite <IReal>(
(Real <double>)(
TDistribution.AStudT(alpha, pointsCount - 2)
)
)
+
new IntervalLeftInfiniteRightOpen <IReal>(
(Real <double>)(
TDistribution.AStudT(alpha, pointsCount - 2)
)
))
)
);
}
public static double Student(double significance_level, int degrees_of_freedom)
{
var td = new TDistribution(degrees_of_freedom);
return(Math.Abs(td.InverseDistributionFunction(significance_level)));
}
/// <summary>
/// Returns a new line chart plotting the specified function of the given distribution for 0.0001 <= p <= 0.9999.
/// </summary>
/// <param name="dist">The distribution.</param>
/// <param name="function">The distribution function to plot.</param>
/// <param name="numInterpolatedValues">The number of interpolated values.</param>
/// <returns>A new chart.</returns>
public static ChartControl ToChart( TDistribution dist, DistributionFunction function = DistributionFunction.PDF, int numInterpolatedValues = 100 )
{
ChartControl chart = GetDefaultChart();
Update( ref chart, dist, function, numInterpolatedValues );
return chart;
}
/// <summary>
/// Updates the given chart with the specified distribution.
/// </summary>
/// <param name="chart">A chart.</param>
/// <param name="dist">The distribution.</param>
/// <param name="function">The distribution function to plot.</param>
/// <param name="numInterpolatedValues">The number of interpolated values.</param>
/// <returns>A new chart.</returns>
/// <remarks>
/// Plots the specified function of the given distribution for 0.0001 <= p <= 0.9999.
/// <br/>
/// Titles are added only if chart does not currently contain any titles.
/// <br/>
/// chart.Series[0] is replaced, or added if necessary.
/// </remarks>
public static void Update( ref ChartControl chart, TDistribution dist, DistributionFunction function = DistributionFunction.PDF, int numInterpolatedValues = 100 )
{
List<string> titles = new List<string>()
{
"TDistribution",
String.Format("df={0}", dist.DegreesOfFreedom)
};
UpdateContinuousDistribution( ref chart, dist, titles, function, numInterpolatedValues );
}
/// <summary>
/// Shows a new chart in a default form.
/// </summary>
/// <param name="dist">The distribution.</param>
/// <param name="function">The distribution function to plot.</param>
/// <param name="numInterpolatedValues">The number of interpolated values.</param>
/// <remarks>
/// Equivalent to:
/// <code>
/// NMathStatsChart.Show( ToChart( dist, function, numInterpolatedValues ) );
/// </code>
/// </remarks>
public static void Show( TDistribution dist, DistributionFunction function = DistributionFunction.PDF, int numInterpolatedValues = 100 )
{
Show( ToChart( dist, function, numInterpolatedValues ) );
}
public ProcessingReturnValues FitAndPlotSlowMotion(
Dictionary <int, SingleMultiFrameMeasurement> measurements,
FlybyMeasurementContext meaContext,
GetProcessingValueCallback getValueCallback,
Graphics g, FlybyPlottingContext plottingContext, float xScale, float yScale, int imageWidth)
{
// Compute median, use median based exclusion rules
// Report the median position for the time at the middle of the measured interval
// Do not expect elongated image (no corrections from the exposure)
// May apply instrumental delay corrections for the frame time
var rv = new ProcessingReturnValues();
double sum = 0;
double userSum = 0;
double stdDevUserSum = 0;
int numFramesUser = 0;
double userMidFrom = meaContext.UserMidValue - meaContext.MaxStdDev;
double userMidTo = meaContext.UserMidValue + meaContext.MaxStdDev;
rv.EarliestFrame = int.MaxValue;
rv.LatestFrame = int.MinValue;
List <double> medianList = new List <double>();
List <double> medianWeightsList = new List <double>();
var minPosUncertaintyArcSec = TangraConfig.Settings.Astrometry.AssumedPositionUncertaintyPixels * meaContext.ArsSecsInPixel;
foreach (SingleMultiFrameMeasurement measurement in measurements.Values)
{
float x = (measurement.FrameNo - meaContext.MinFrameNo) * xScale + 5;
ProcessingValues val = getValueCallback(measurement);
double valueFrom = val.Value - val.StdDev;
double valueTo = val.Value + val.StdDev;
float yFrom = (float)(valueFrom - plottingContext.MinValue) * yScale + 5;
float yTo = (float)(valueTo - plottingContext.MinValue) * yScale + 5;
sum += val.Value;
Pen mPen = plottingContext.IncludedPen;
if (!double.IsNaN(meaContext.UserMidValue))
{
if ((valueFrom >= userMidFrom && valueFrom <= userMidTo) ||
(valueTo >= userMidFrom && valueTo <= userMidTo))
{
numFramesUser++;
userSum += val.Value;
medianList.Add(val.Value);
medianWeightsList.Add(ComputePositionWeight(val.StdDev, measurement, minPosUncertaintyArcSec, WeightingMode.SNR));
stdDevUserSum += val.StdDev * val.StdDev;
if (rv.EarliestFrame > measurement.FrameNo)
{
rv.EarliestFrame = measurement.FrameNo;
}
if (rv.LatestFrame < measurement.FrameNo)
{
rv.LatestFrame = measurement.FrameNo;
}
}
else
{
mPen = plottingContext.ExcludedPen;
}
}
g.DrawLine(mPen, x, yFrom, x, yTo);
g.DrawLine(mPen, x - 1, yFrom, x + 1, yFrom);
g.DrawLine(mPen, x - 1, yTo, x + 1, yTo);
}
if (!double.IsNaN(meaContext.UserMidValue) && numFramesUser > 0)
{
double average = userSum / numFramesUser;
double err = Math.Sqrt(stdDevUserSum) / (numFramesUser - 1);
float yAve = (float)(average - plottingContext.MinValue) * yScale + 5;
g.DrawLine(plottingContext.AveragePen, 5, yAve - 1, imageWidth - 5, yAve - 1);
g.DrawLine(plottingContext.AveragePen, 5, yAve, imageWidth - 5, yAve);
g.DrawLine(plottingContext.AveragePen, 5, yAve + 1, imageWidth - 5, yAve + 1);
float yMin = (float)(userMidFrom - plottingContext.MinValue) * yScale + 5;
float yMax = (float)(userMidTo - plottingContext.MinValue) * yScale + 5;
g.DrawLine(plottingContext.AveragePen, 5, yMin, imageWidth - 5, yMin);
g.DrawLine(plottingContext.AveragePen, 5, yMax, imageWidth - 5, yMax);
double median;
double medianWeight;
WeightedMedian(Tuple.Create(medianList, medianWeightsList), out median, out medianWeight);
double standardMedian = medianList.Median();
Trace.WriteLine(string.Format("{0}; Included: {1}; Average: {2}; Wighted Median: {3}; Standard Median: {4}",
meaContext.UserMidValue.ToString("0.00000"),
numFramesUser, AstroConvert.ToStringValue(average, "+HH MM SS.TTT"),
AstroConvert.ToStringValue(median, "+HH MM SS.TTT"),
AstroConvert.ToStringValue(standardMedian, "+HH MM SS.TTT")));
rv.FittedValue = median;
var stdDevArcSec = 3600 * Math.Sqrt(medianList.Sum(x => (x - median) * (x - median)) / (medianList.Count - 1));
var tCoeff95 = TDistribution.CalculateCriticalValue(medianList.Count, (1 - 0.95), 0.0001);
var error95 = 1.253 * tCoeff95 * stdDevArcSec / Math.Sqrt(medianList.Count);
rv.FittedValueUncertaintyArcSec = error95;
rv.IsVideoNormalPosition = false;
}
else
{
double average = sum / measurements.Count;
float yAve = (float)(average - plottingContext.MinValue) * yScale + 5;
g.DrawLine(Pens.WhiteSmoke, 5, yAve, imageWidth - 5, yAve);
rv.FittedValue = double.NaN;
}
return(rv);
}
public void MedianTest()
{
TDistribution target = new TDistribution(7.6);
Assert.AreEqual(target.Median, target.InverseDistributionFunction(0.5));
}
