public void KendallNullDistributionTest()
{
// pick independent distributions for x and y, which needn't be normal and needn't be related
Distribution xDistrubtion = new LogisticDistribution();
Distribution yDistribution = new ExponentialDistribution();
Random rng = new Random(314159265);
// generate bivariate samples of various sizes
//int n = 64; {
foreach (int n in TestUtilities.GenerateIntegerValues(4, 64, 8)) {
Sample testStatistics = new Sample();
Distribution testDistribution = null;
for (int i = 0; i < 128; i++) {
BivariateSample sample = new BivariateSample();
for (int j = 0; j < n; j++) {
sample.Add(xDistrubtion.GetRandomValue(rng), yDistribution.GetRandomValue(rng));
}
TestResult result = sample.KendallTauTest();
testStatistics.Add(result.Statistic);
testDistribution = result.Distribution;
}
//TestResult r2 = testStatistics.KolmogorovSmirnovTest(testDistribution);
//Console.WriteLine("n={0} P={1}", n, r2.LeftProbability);
//Assert.IsTrue(r2.RightProbability > 0.05);
Console.WriteLine("{0} {1}", testStatistics.PopulationVariance, testDistribution.Variance);
Assert.IsTrue(testStatistics.PopulationMean.ConfidenceInterval(0.95).ClosedContains(testDistribution.Mean));
Assert.IsTrue(testStatistics.PopulationVariance.ConfidenceInterval(0.95).ClosedContains(testDistribution.Variance));
}
}
public void ContingencyTableProbabilitiesAndUncertainties()
{
// start with an underlying population
double[,] pp = new double[,]
{ { 1.0 / 45.0, 2.0 / 45.0, 3.0 / 45.0 },
{ 4.0 / 45.0, 5.0 / 45.0, 6.0 / 45.0 },
{ 7.0 / 45.0, 8.0 / 45.0, 9.0 / 45.0 } };
// form 50 contingency tables, each with N = 50
Random rng = new Random(314159);
BivariateSample p22s = new BivariateSample();
BivariateSample pr0s = new BivariateSample();
BivariateSample pc1s = new BivariateSample();
BivariateSample pr2c0s = new BivariateSample();
BivariateSample pc1r2s = new BivariateSample();
for (int i = 0; i < 50; i++) {
ContingencyTable T = new ContingencyTable(3, 3);
for (int j = 0; j < 50; j++) {
int r, c;
ChooseRandomCell(pp, rng.NextDouble(), out r, out c);
T.Increment(r, c);
}
Assert.IsTrue(T.Total == 50);
// for each contingency table, compute estimates of various population quantities
UncertainValue p22 = T.Probability(2, 2);
UncertainValue pr0 = T.ProbabilityOfRow(0);
UncertainValue pc1 = T.ProbabilityOfColumn(1);
UncertainValue pr2c0 = T.ProbabilityOfRowConditionalOnColumn(2, 0);
UncertainValue pc1r2 = T.ProbabilityOfColumnConditionalOnRow(1, 2);
p22s.Add(p22.Value, p22.Uncertainty);
pr0s.Add(pr0.Value, pr0.Uncertainty);
pc1s.Add(pc1.Value, pc1.Uncertainty);
pr2c0s.Add(pr2c0.Value, pr2c0.Uncertainty);
pc1r2s.Add(pc1r2.Value, pc1r2.Uncertainty);
}
// the estimated population mean of each probability should include the correct probability in the underlyting distribution
Assert.IsTrue(p22s.X.PopulationMean.ConfidenceInterval(0.95).ClosedContains(9.0 / 45.0));
Assert.IsTrue(pr0s.X.PopulationMean.ConfidenceInterval(0.95).ClosedContains(6.0 / 45.0));
Assert.IsTrue(pc1s.X.PopulationMean.ConfidenceInterval(0.95).ClosedContains(15.0 / 45.0));
Assert.IsTrue(pr2c0s.X.PopulationMean.ConfidenceInterval(0.95).ClosedContains(7.0 / 12.0));
Assert.IsTrue(pc1r2s.X.PopulationMean.ConfidenceInterval(0.95).ClosedContains(8.0 / 24.0));
// the estimated uncertainty for each population parameter should be the standard deviation across independent measurements
// since the reported uncertainly changes each time, we use the mean value for comparison
Assert.IsTrue(p22s.X.PopulationStandardDeviation.ConfidenceInterval(0.95).ClosedContains(p22s.Y.Mean));
Assert.IsTrue(pr0s.X.PopulationStandardDeviation.ConfidenceInterval(0.95).ClosedContains(pr0s.Y.Mean));
Assert.IsTrue(pc1s.X.PopulationStandardDeviation.ConfidenceInterval(0.95).ClosedContains(pc1s.Y.Mean));
Assert.IsTrue(pr2c0s.X.PopulationStandardDeviation.ConfidenceInterval(0.95).ClosedContains(pr2c0s.Y.Mean));
Assert.IsTrue(pc1r2s.X.PopulationStandardDeviation.ConfidenceInterval(0.95).ClosedContains(pc1r2s.Y.Mean));
}
public void BivariateLinearPolynomialRegressionAgreement()
{
// A degree-1 polynomial fit should give the same answer as a linear fit
BivariateSample B = new BivariateSample();
B.Add(0.0, 5.0);
B.Add(3.0, 6.0);
B.Add(1.0, 7.0);
B.Add(4.0, 8.0);
B.Add(2.0, 9.0);
FitResult PR = B.PolynomialRegression(1);
FitResult LR = B.LinearRegression();
Assert.IsTrue(TestUtilities.IsNearlyEqual(PR.Parameters, LR.Parameters));
Assert.IsTrue(TestUtilities.IsNearlyEqual(PR.CovarianceMatrix, LR.CovarianceMatrix));
Assert.IsTrue(TestUtilities.IsNearlyEqual(PR.GoodnessOfFit.Statistic, LR.GoodnessOfFit.Statistic));
}
public void BivariateNullAssociation()
{
Random rng = new Random(314159265);
// Create sample sets for our three test statisics
Sample PS = new Sample();
Sample SS = new Sample();
Sample KS = new Sample();
// variables to hold the claimed distribution of teach test statistic
Distribution PD = null;
Distribution SD = null;
Distribution KD = null;
// generate a large number of bivariate samples and conduct our three tests on each
for (int j = 0; j < 100; j++) {
BivariateSample S = new BivariateSample();
// sample size should be large so that asymptotic assumptions are justified
for (int i = 0; i < 100; i++) {
double x = rng.NextDouble();
double y = rng.NextDouble();
S.Add(x, y);
}
TestResult PR = S.PearsonRTest();
PS.Add(PR.Statistic);
PD = PR.Distribution;
TestResult SR = S.SpearmanRhoTest();
SS.Add(SR.Statistic);
SD = SR.Distribution;
TestResult KR = S.KendallTauTest();
KS.Add(KR.Statistic);
KD = KR.Distribution;
}
// do KS to test whether the samples follow the claimed distributions
//Console.WriteLine(PS.KolmogorovSmirnovTest(PD).LeftProbability);
//Console.WriteLine(SS.KolmogorovSmirnovTest(SD).LeftProbability);
//Console.WriteLine(KS.KolmogorovSmirnovTest(KD).LeftProbability);
Assert.IsTrue(PS.KolmogorovSmirnovTest(PD).LeftProbability < 0.95);
Assert.IsTrue(SS.KolmogorovSmirnovTest(SD).LeftProbability < 0.95);
Assert.IsTrue(KS.KolmogorovSmirnovTest(KD).LeftProbability < 0.95);
}
public void BivariatePolynomialRegression()
{
// do a set of polynomial regression fits
// make sure not only that the fit parameters are what they should be, but that their variances/covariances are as claimed
Random rng = new Random(271828);
// define logistic parameters
double[] a = new double[] { 0.0, -1.0, 2.0, -3.0 };
// keep track of sample of returned a and b fit parameters
MultivariateSample A = new MultivariateSample(a.Length);
// also keep track of returned covariance estimates
// since these vary slightly from fit to fit, we will average them
SymmetricMatrix C = new SymmetricMatrix(a.Length);
// also keep track of test statistics
Sample F = new Sample();
// do 100 fits
for (int k = 0; k < 100; k++) {
// we should be able to draw x's from any distribution; noise should be drawn from a normal distribution
Distribution xd = new CauchyDistribution();
Distribution nd = new NormalDistribution(0.0, 4.0);
// generate a synthetic data set
BivariateSample s = new BivariateSample();
for (int j = 0; j < 20; j++) {
double x = xd.GetRandomValue(rng);
double y = nd.GetRandomValue(rng);
for (int i = 0; i < a.Length; i++) {
y += a[i] * MoreMath.Pow(x, i);
}
s.Add(x, y);
}
// do the regression
FitResult r = s.PolynomialRegression(a.Length - 1);
ColumnVector ps = r.Parameters;
//Console.WriteLine("{0} {1} {2}", ps[0], ps[1], ps[2]);
// record best fit parameters
A.Add(ps);
// record estimated covariances
C += r.CovarianceMatrix;
// record the fit statistic
F.Add(r.GoodnessOfFit.Statistic);
//Console.WriteLine("F={0}", r.GoodnessOfFit.Statistic);
}
C = (1.0 / A.Count) * C; // allow matrix division by real numbers
// check that mean parameter estimates are what they should be: the underlying population parameters
for (int i = 0; i < A.Dimension; i++) {
Console.WriteLine("{0} {1}", A.Column(i).PopulationMean, a[i]);
Assert.IsTrue(A.Column(i).PopulationMean.ConfidenceInterval(0.95).ClosedContains(a[i]));
}
// check that parameter covarainces are what they should be: the reported covariance estimates
for (int i = 0; i < A.Dimension; i++) {
for (int j = i; j < A.Dimension; j++) {
Console.WriteLine("{0} {1} {2} {3}", i, j, C[i, j], A.TwoColumns(i, j).PopulationCovariance);
Assert.IsTrue(A.TwoColumns(i, j).PopulationCovariance.ConfidenceInterval(0.95).ClosedContains(C[i, j]));
}
}
// check that F is distributed as it should be
//Console.WriteLine(fs.KolmogorovSmirnovTest(new FisherDistribution(2, 48)).LeftProbability);
}
public void BivariateLinearRegressionGoodnessOfFitDistribution()
{
// create uncorrelated x and y values
// the distribution of F-test statistics returned by linear fits should follow the expected F-distribution
Random rng = new Random(987654321);
NormalDistribution xd = new NormalDistribution(1.0, 2.0);
NormalDistribution yd = new NormalDistribution(-3.0, 4.0);
Sample fs = new Sample();
for (int i = 0; i < 127; i++) {
BivariateSample xys = new BivariateSample();
for (int j = 0; j < 7; j++) {
xys.Add(xd.GetRandomValue(rng), yd.GetRandomValue(rng));
}
double f = xys.LinearRegression().GoodnessOfFit.Statistic;
fs.Add(f);
}
Distribution fd = new FisherDistribution(1, 5);
Console.WriteLine("{0} v. {1}", fs.PopulationMean, fd.Mean);
TestResult t = fs.KolmogorovSmirnovTest(fd);
Console.WriteLine(t.LeftProbability);
Assert.IsTrue(t.LeftProbability < 0.95);
}
public void NormalFitUncertainties()
{
NormalDistribution N = new NormalDistribution(-1.0, 2.0);
// Create a bivariate sample to hold our fitted best mu and sigma values
// so we can determine their covariance as well as their means and variances
BivariateSample fits = new BivariateSample();
double cmm = 0.0, css = 0.0, cms = 0.0;
// A bunch of times, create a normal sample
for (int i = 0; i < 64; i++) {
// we will use small samples so the variation in mu and sigma will be more substantial
Sample s = TestUtilities.CreateSample(N, 16, i);
// fit each sample to a normal distribution
FitResult fit = NormalDistribution.FitToSample(s);
// and record the mu and sigma values from the fit into our bivariate sample
fits.Add(fit.Parameter(0).Value, fit.Parameter(1).Value);
// also record the claimed covariances among these parameters
cmm += fit.Covariance(0, 0); css += fit.Covariance(1, 1); cms += fit.Covariance(0, 1);
}
cmm /= fits.Count; css /= fits.Count; cms /= fits.Count;
// the mean fit values should agree with the population distribution
Console.WriteLine("{0} {1}", fits.X.PopulationMean, N.Mean);
Assert.IsTrue(fits.X.PopulationMean.ConfidenceInterval(0.95).ClosedContains(N.Mean));
Console.WriteLine("{0} {1}", fits.Y.PopulationMean, N.StandardDeviation);
Assert.IsTrue(fits.Y.PopulationMean.ConfidenceInterval(0.95).ClosedContains(N.StandardDeviation));
// but also the covariances of those fit values should agree with the claimed covariances
Console.WriteLine("{0} {1}", fits.X.PopulationVariance, cmm);
Assert.IsTrue(fits.X.PopulationVariance.ConfidenceInterval(0.95).ClosedContains(cmm));
Console.WriteLine("{0} {1}", fits.Y.PopulationVariance, css);
Assert.IsTrue(fits.Y.PopulationVariance.ConfidenceInterval(0.95).ClosedContains(css));
Console.WriteLine("{0} {1}", fits.PopulationCovariance, cms);
Assert.IsTrue(fits.PopulationCovariance.ConfidenceInterval(0.95).ClosedContains(cms));
/*
Random rng = new Random(2718281);
BivariateSample P = new BivariateSample();
double cmm = 0.0;
double css = 0.0;
double cms = 0.0;
for (int i = 0; i < 64; i++) {
Sample s = new Sample();
for (int j = 0; j < 16; j++) {
s.Add(N.GetRandomValue(rng));
}
FitResult r = NormalDistribution.FitToSample(s);
P.Add(r.Parameter(0).Value, r.Parameter(1).Value);
cmm += r.Covariance(0, 0);
css += r.Covariance(1, 1);
cms += r.Covariance(0, 1);
}
cmm /= P.Count;
css /= P.Count;
cms /= P.Count;
Console.WriteLine("{0} {1}", P.X.PopulationMean, P.Y.PopulationMean);
Assert.IsTrue(P.X.PopulationMean.ConfidenceInterval(0.95).ClosedContains(N.Mean));
Assert.IsTrue(P.Y.PopulationMean.ConfidenceInterval(0.95).ClosedContains(N.StandardDeviation));
Assert.IsTrue(P.X.PopulationVariance.ConfidenceInterval(0.95).ClosedContains(cmm));
Assert.IsTrue(P.Y.PopulationVariance.ConfidenceInterval(0.95).ClosedContains(css));
Assert.IsTrue(P.PopulationCovariance.ConfidenceInterval(0.95).ClosedContains(cms));
*/
}
public void PearsonRDistribution()
{
Random rng = new Random(1);
// pick some underlying distributions for the sample variables, which must be normal but can have any parameters
NormalDistribution xDistribution = new NormalDistribution(1, 2);
NormalDistribution yDistribution = new NormalDistribution(3, 4);
// try this for several sample sizes, all low so that we see the difference from the normal distribution
// n = 3 maxima at ends; n = 4 uniform; n = 5 semi-circular "mound"; n = 6 parabolic "mound"
foreach (int n in new int[] { 3, 4, 5, 6, 8 }) {
Console.WriteLine("n={0}", n);
// find r values
Sample rSample = new Sample();
for (int i = 0; i < 100; i++) {
// to get each r value, construct a bivariate sample of the given size with no cross-correlation
BivariateSample xySample = new BivariateSample();
for (int j = 0; j < n; j++) {
xySample.Add(xDistribution.GetRandomValue(rng), yDistribution.GetRandomValue(rng));
}
double r = xySample.PearsonRTest().Statistic;
rSample.Add(r);
}
// check whether r is distributed as expected
TestResult result = rSample.KolmogorovSmirnovTest(new PearsonRDistribution(n));
Console.WriteLine("P={0}", result.LeftProbability);
Assert.IsTrue(result.LeftProbability < 0.95);
}
}
public void BivariateSampleManipulations()
{
BivariateSample s = new BivariateSample();
s.Add(1.0, 3.0);
s.Add(2.0, 2.0);
s.Add(3.0, 1.0);
Assert.IsTrue(s.Count == 3);
Assert.IsTrue(s.Remove(2.0, 2.0));
Assert.IsTrue(s.Count == 2);
Assert.IsFalse(s.Remove(2.0, 2.0));
Assert.IsTrue(s.Contains(1.0, 3.0));
Assert.IsFalse(s.Contains(3.0, 3.0));
s.Clear();
Assert.IsTrue(s.Count == 0);
}
public void WaldFitUncertainties()
{
WaldDistribution wald = new WaldDistribution(3.5, 2.5);
Random rng = new Random(314159);
BivariateSample P = new BivariateSample();
double cmm = 0.0;
double css = 0.0;
double cms = 0.0;
for (int i = 0; i < 50; i++) {
Sample s = new Sample();
for (int j = 0; j < 50; j++) {
s.Add(wald.GetRandomValue(rng));
}
FitResult r = WaldDistribution.FitToSample(s);
P.Add(r.Parameter(0).Value, r.Parameter(1).Value);
cmm += r.Covariance(0, 0);
css += r.Covariance(1, 1);
cms += r.Covariance(0, 1);
}
cmm /= P.Count;
css /= P.Count;
cms /= P.Count;
Console.WriteLine("{0} {1}", P.X.PopulationMean, P.Y.PopulationMean);
Assert.IsTrue(P.X.PopulationMean.ConfidenceInterval(0.95).ClosedContains(wald.Mean));
Assert.IsTrue(P.Y.PopulationMean.ConfidenceInterval(0.95).ClosedContains(wald.ShapeParameter));
// the ML shape parameter estimate appears to be asymptoticly unbiased, as it must be according to ML fit theory,
// but detectably upward biased for small n. we now correct for this.
Console.WriteLine("{0} {1} {2}", P.X.PopulationVariance, P.Y.PopulationVariance, P.PopulationCovariance);
Console.WriteLine("{0} {1} {2}", cmm, css, cms);
Assert.IsTrue(P.X.PopulationVariance.ConfidenceInterval(0.95).ClosedContains(cmm));
Assert.IsTrue(P.Y.PopulationVariance.ConfidenceInterval(0.95).ClosedContains(css));
Assert.IsTrue(P.PopulationCovariance.ConfidenceInterval(0.95).ClosedContains(cms));
}
/// <summary>
/// Beta arvutus
/// </summary>
/// <param name="finDataAdapter">Adapter kõigi finantsandmete kättesaamise jaoks</param>
/// <param name="dcfInput">DCF arvutuste eelduste hoidja</param>
public static void CalculateBeta(FinDataAdapter finDataAdapter, DcfInput dcfInput)
{
BivariateSample bivariate = new BivariateSample();
MultivariateSample mv = new MultivariateSample(2);
decimal prevPrice = 0;
double? prevIndex = null;
decimal curPrice = 0;
double? curIndex = null;
int k = 0;
for (int i = 0; i < finDataAdapter.PriceDataDao.PriceDatas.Count; i = i + 22)
{
if (k < 36)
{
PriceData pd = finDataAdapter.PriceDataDao.PriceDatas[i];
curPrice = pd.AdjClose;
curIndex = finDataAdapter.PriceDataDao.GetClosePrice(pd.PriceDate, finDataAdapter.PriceDataDao.IndexDatas)[0];
if (curPrice != 0 && curIndex != null && prevPrice != 0 && prevIndex != null)
{
//MessageBox.Show("s:" + ((double)(prevPrice / curPrice) - 1));
//MessageBox.Show("i:" + ((double)(prevIndex / curIndex) - 1));
////bivariate.Add((double) (prevPrice/curPrice)-1,(double) (prevIndex/curIndex)-1);
double[] db = new double[2];
db[0] = ((double)(prevPrice / curPrice) - 1);
db[1] = ((double)(prevIndex / curIndex) - 1);
mv.Add(db);
}
prevPrice = curPrice;
prevIndex = curIndex;
//DateTime dt = finDataAdapter.PriceDataDao.PriceDatas[i].PriceDate;
//MessageBox.Show(finDataAdapter.PriceDataDao.PriceDatas[i].AdjClose + " " +
// dt.ToShortDateString());
//MessageBox.Show(finDataAdapter.PriceDataDao.GetClosePrice(dt, finDataAdapter.PriceDataDao.IndexDatas)[0].ToString());
}
k++;
}
if (mv.Count > 10)
{
//FitResult fitResult = bivariate.LinearRegression();
FitResult fitResult = mv.LinearRegression(0);
dcfInput.Beta = fitResult.Parameter(1).Value;
List<FinData> finDatas = finDataAdapter.FinDataDao.FinDatas;
dcfInput.CostOfEquity = dcfInput.RiskFreeRate + dcfInput.Beta * dcfInput.MarketRiskPremium;
double debt = 0;
if (finDatas[finDatas.Count - 1].BsCurrentPortionOfLongTermDebt != null)
{
debt += (double)finDatas[finDatas.Count - 1].BsCurrentPortionOfLongTermDebt;
}
if (finDatas[finDatas.Count - 1].BsTotalLongTermDebt != null)
{
debt += (double)finDatas[finDatas.Count - 1].BsTotalLongTermDebt;
}
double total = 0.0;
if (finDatas[finDatas.Count - 1].BsShareholdersEquity1 != null)
{
total += (double)(finDatas[finDatas.Count - 1].BsShareholdersEquity1);
}
total += debt;
try
{
dcfInput.Wacc = dcfInput.CostOfEquity *
(double)(finDatas[finDatas.Count - 1].BsShareholdersEquity1 / total) +
dcfInput.CostOfDebt * (double)(debt / total) * (1 - dcfInput.TaxRate);
}
catch (InvalidOperationException) { }
//MessageBox.Show("beta: "+fitResult.Parameter(1).Value.ToString());
//double[] pars = fitResult.Parameters();
//foreach (var par in pars)
//{
// MessageBox.Show(par.ToString());
//}
//MessageBox.Show(fitResult.CorrelationCoefficient(0,1).ToString());
//double[] gfit = fitResult.
//MessageBox.Show(fitResult.);
//MessageBox.Show(fitResult.Parameter(2).ToString());
}
}
public void Bug6162()
{
// When UncertianMeasurementSample.FitToPolynomial used Cholesky inversion of (A^T A), this inversion
// would fail when roundoff errors would made the matrix non-positive-definite. We have now changed
// to QR decomposition, which is more robust.
//real data
double[] X_axis = new double[] { 40270.65625, 40270.6569444444, 40270.6576388888, 40270.6583333332, 40270.6590277776,
40270.659722222, 40270.6604166669, 40270.6611111113, 40270.6618055557, 40270.6625000001 };
double[] Y_axis = new double[] { 246.824996948242, 246.850006103516, 245.875, 246.225006103516, 246.975006103516,
247.024993896484, 246.949996948242, 246.875, 247.5, 247.100006103516 };
UncertainMeasurementSample DataSet = new UncertainMeasurementSample();
for (int i = 0; i < 10; i++) DataSet.Add(X_axis[i], Y_axis[i], 1);
//for (int i = 0; i < 10; i++) DataSet.Add(X_axis[i] - 40270.0, Y_axis[i] - 247.0, 1);
FitResult DataFit = DataSet.FitToPolynomial(3);
for (int i = 0; i < DataFit.Dimension; i++)
Console.WriteLine("a" + i.ToString() + " = " + DataFit.Parameter(i).Value);
BivariateSample bs = new BivariateSample();
for (int i = 0; i < 10; i++) bs.Add(X_axis[i], Y_axis[i]);
FitResult bsFit = bs.PolynomialRegression(3);
for (int i = 0; i < bsFit.Dimension; i++) Console.WriteLine(bsFit.Parameter(i));
}
// Not fixing this bug; use Polynomial interpolation for this scenario instead
//[TestMethod]
public void Bug6392()
{
// bug requests that we support regression with number of points equal to number
// of fit parameters, i.e. polynomial fit
var biSample = new BivariateSample();
biSample.Add(0, 1);
biSample.Add(1, -1);
var fitResult = biSample.LinearRegression();
}
public void SpearmanNullDistributionTest()
{
// pick independent distributions for x and y, which needn't be normal and needn't be related
Distribution xDistrubtion = new UniformDistribution();
Distribution yDistribution = new CauchyDistribution();
Random rng = new Random(1);
// generate bivariate samples of various sizes
foreach (int n in TestUtilities.GenerateIntegerValues(4, 64, 8)) {
Sample testStatistics = new Sample();
Distribution testDistribution = null;
for (int i = 0; i < 128; i++) {
BivariateSample sample = new BivariateSample();
for (int j = 0; j < n; j++) {
sample.Add(xDistrubtion.GetRandomValue(rng), yDistribution.GetRandomValue(rng));
}
TestResult result = sample.SpearmanRhoTest();
testStatistics.Add(result.Statistic);
testDistribution = result.Distribution;
}
TestResult r2 = testStatistics.KuiperTest(testDistribution);
Console.WriteLine("n={0} P={1}", n, r2.LeftProbability);
Assert.IsTrue(r2.RightProbability > 0.05);
Assert.IsTrue(testStatistics.PopulationMean.ConfidenceInterval(0.99).ClosedContains(testDistribution.Mean));
Assert.IsTrue(testStatistics.PopulationVariance.ConfidenceInterval(0.99).ClosedContains(testDistribution.Variance));
}
}
public void PairedStudentTTest()
{
BivariateSample s = new BivariateSample();
s.Add(3, 5);
s.Add(0, 1);
s.Add(6, 5);
s.Add(7, 7);
s.Add(4, 10);
s.Add(3, 9);
s.Add(2, 7);
s.Add(1, 11);
s.Add(4, 8);
Console.WriteLine(s.Count);
TestResult r = s.PairedStudentTTest();
Console.WriteLine(r.Statistic);
Console.WriteLine(r.LeftProbability);
}
public void BivariateSampleCopy()
{
// test independency of copy
BivariateSample sample1 = new BivariateSample();
sample1.Add(1.0, 2.0);
BivariateSample sample2 = sample1.Copy();
sample2.Add(3.0, 4.0);
Assert.IsTrue(sample1.Count == 1);
Assert.IsTrue(sample2.Count == 2);
}
public void BivariateSampleEnumerations()
{
List<XY> points = new List<XY>(new XY[] { new XY(1.0, 2.0), new XY(2.0, 3.0), new XY(3.0, 4.0) });
BivariateSample sample = new BivariateSample();
sample.Add(points);
Assert.IsTrue(sample.Count == points.Count);
foreach (XY point in sample) {
Assert.IsTrue(points.Remove(point));
}
Assert.IsTrue(points.Count == 0);
}
public void WeibullFitUncertainties()
{
// check that the uncertainty in reported fit parameters is actually meaningful
// it should be the standard deviation of fit parameter values in a sample of many fits
// define a population distribution
Distribution distribution = new WeibullDistribution(2.5, 1.5);
// draw a lot of samples from it; fit each sample and
// record the reported parameter value and error of each
BivariateSample values = new BivariateSample();
MultivariateSample uncertainties = new MultivariateSample(3);
for (int i = 0; i < 50; i++) {
Sample sample = CreateSample(distribution, 10, i);
FitResult fit = WeibullDistribution.FitToSample(sample);
UncertainValue a = fit.Parameter(0);
UncertainValue b = fit.Parameter(1);
values.Add(a.Value, b.Value);
uncertainties.Add(a.Uncertainty, b.Uncertainty, fit.Covariance(0,1));
}
// the reported errors should agree with the standard deviation of the reported parameters
Assert.IsTrue(values.X.PopulationStandardDeviation.ConfidenceInterval(0.95).ClosedContains(uncertainties.Column(0).Mean));
Assert.IsTrue(values.Y.PopulationStandardDeviation.ConfidenceInterval(0.95).ClosedContains(uncertainties.Column(1).Mean));
//Console.WriteLine("{0} {1}", values.PopulationCovariance, uncertainties.Column(2).Mean);
//Assert.IsTrue(values.PopulationCovariance.ConfidenceInterval(0.95).ClosedContains(uncertainties.Column(2).Mean));
}
public void LinearLogisticRegression()
{
// do a set of logistic regression fits
// make sure not only that the fit parameters are what they should be, but that their variances/covariances are as returned
Random rng = new Random(314159);
// define logistic parameters
double a0 = 1.0; double b0 = -1.0 / 2.0;
//double a0 = -0.5; double b0 = 2.0;
// keep track of sample of returned a and b fit parameters
BivariateSample ps = new BivariateSample();
// also keep track of returned covariance estimates
// since these vary slightly from fit to fit, we will average them
double caa = 0.0;
double cbb = 0.0;
double cab = 0.0;
// do 50 fits
for (int k = 0; k < 50; k++) {
Console.WriteLine("k={0}", k);
// generate a synthetic data set
BivariateSample s = new BivariateSample();
for (int i = 0; i < 50; i++) {
double x = 2.0 * rng.NextDouble() - 1.0;
double ez = Math.Exp(a0 + b0 * x);
double P = ez / (1.0 + ez);
if (rng.NextDouble() < P) {
s.Add(x, 1.0);
} else {
s.Add(x, 0.0);
}
}
//if (k != 27) continue;
// do the regression
FitResult r = s.LinearLogisticRegression();
// record best fit parameters
double a = r.Parameter(0).Value;
double b = r.Parameter(1).Value;
ps.Add(a, b);
Console.WriteLine("{0}, {1}", a, b);
// record estimated covariances
caa += r.Covariance(0, 0);
cbb += r.Covariance(1, 1);
cab += r.Covariance(0, 1);
}
caa /= ps.Count;
cbb /= ps.Count;
cab /= ps.Count;
// check that mean parameter estimates are what they should be: the underlying population parameters
Assert.IsTrue(ps.X.PopulationMean.ConfidenceInterval(0.95).ClosedContains(a0));
Assert.IsTrue(ps.Y.PopulationMean.ConfidenceInterval(0.95).ClosedContains(b0));
// check that parameter covarainces are what they should be: the reported covariance estimates
Assert.IsTrue(ps.X.PopulationVariance.ConfidenceInterval(0.95).ClosedContains(caa));
Assert.IsTrue(ps.Y.PopulationVariance.ConfidenceInterval(0.95).ClosedContains(cbb));
Assert.IsTrue(ps.PopulationCovariance.ConfidenceInterval(0.95).ClosedContains(cab));
}
public void BivariateLogisticRegression()
{
double[] c = new double[] { -0.1, 1.0 };
Random rng = new Random(1);
UniformDistribution pointDistribution = new UniformDistribution(Interval.FromEndpoints(-4.0, 4.0));
BivariateSample sample1 = new BivariateSample();
MultivariateSample sample2 = new MultivariateSample(2);
for (int k = 0; k < 1000; k++) {
double x = pointDistribution.GetRandomValue(rng);
double z = c[0] * x + c[1];
double ez = Math.Exp(z);
double p = ez / (1.0 + ez);
double y = (rng.NextDouble() < p) ? 1.0 : 0.0;
sample1.Add(x, y);
sample2.Add(x, y);
}
Console.WriteLine(sample1.Covariance / sample1.X.Variance / sample1.Y.Mean / (1.0 - sample1.Y.Mean));
Console.WriteLine(sample1.Covariance / sample1.X.Variance / sample1.Y.Variance);
FitResult result1 = sample1.LinearLogisticRegression();
FitResult result2 = sample2.TwoColumns(0, 1).LinearLogisticRegression();
FitResult result3 = sample2.LogisticLinearRegression(1);
for (int i = 0; i < result1.Dimension; i++) {
Console.WriteLine("{0} {1} {2}", i, result1.Parameter(i), result3.Parameter(i) );
}
}
public void BivariateLinearRegression()
{
// do a set of logistic regression fits
// make sure not only that the fit parameters are what they should be, but that their variances/covariances are as returned
Random rng = new Random(314159);
// define logistic parameters
double a0 = 2.0; double b0 = -1.0;
// keep track of sample of returned a and b fit parameters
BivariateSample ps = new BivariateSample();
// also keep track of returned covariance estimates
// since these vary slightly from fit to fit, we will average them
double caa = 0.0;
double cbb = 0.0;
double cab = 0.0;
// also keep track of test statistics
Sample fs = new Sample();
// do 100 fits
for (int k = 0; k < 100; k++) {
// we should be able to draw x's from any distribution; noise should be drawn from a normal distribution
Distribution xd = new LogisticDistribution();
Distribution nd = new NormalDistribution(0.0, 2.0);
// generate a synthetic data set
BivariateSample s = new BivariateSample();
for (int i = 0; i < 25; i++) {
double x = xd.GetRandomValue(rng);
double y = a0 + b0 * x + nd.GetRandomValue(rng);
s.Add(x, y);
}
// do the regression
FitResult r = s.LinearRegression();
// record best fit parameters
double a = r.Parameter(0).Value;
double b = r.Parameter(1).Value;
ps.Add(a, b);
// record estimated covariances
caa += r.Covariance(0, 0);
cbb += r.Covariance(1, 1);
cab += r.Covariance(0, 1);
// record the fit statistic
fs.Add(r.GoodnessOfFit.Statistic);
Console.WriteLine("F={0}", r.GoodnessOfFit.Statistic);
}
caa /= ps.Count;
cbb /= ps.Count;
cab /= ps.Count;
// check that mean parameter estimates are what they should be: the underlying population parameters
Assert.IsTrue(ps.X.PopulationMean.ConfidenceInterval(0.95).ClosedContains(a0));
Assert.IsTrue(ps.Y.PopulationMean.ConfidenceInterval(0.95).ClosedContains(b0));
Console.WriteLine("{0} {1}", caa, ps.X.PopulationVariance);
Console.WriteLine("{0} {1}", cbb, ps.Y.PopulationVariance);
// check that parameter covarainces are what they should be: the reported covariance estimates
Assert.IsTrue(ps.X.PopulationVariance.ConfidenceInterval(0.95).ClosedContains(caa));
Assert.IsTrue(ps.Y.PopulationVariance.ConfidenceInterval(0.95).ClosedContains(cbb));
Assert.IsTrue(ps.PopulationCovariance.ConfidenceInterval(0.95).ClosedContains(cab));
// check that F is distributed as it should be
Console.WriteLine(fs.KolmogorovSmirnovTest(new FisherDistribution(2, 48)).LeftProbability);
}
public void GammaFitUncertainty()
{
// check that the uncertainty in reported fit parameters is actually meaningful
// it should be the standard deviation of fit parameter values in a sample of many fits
// define a population distribution
Distribution distribution = new GammaDistribution(1.5, 2.0);
// draw a lot of samples from it; fit each sample and
// record the reported parameter value and error of each
BivariateSample values = new BivariateSample();
BivariateSample uncertainties = new BivariateSample();
for (int i = 0; i < 100; i++) {
Sample sample = CreateSample(distribution, 50, i);
FitResult fit = GammaDistribution.FitToSample(sample);
UncertainValue a = fit.Parameter(0);
UncertainValue b = fit.Parameter(1);
values.Add(a.Value, b.Value);
uncertainties.Add(a.Uncertainty, b.Uncertainty);
}
// the reported errors should agree with the standard deviation of the reported parameters
Assert.IsTrue(values.X.PopulationStandardDeviation.ConfidenceInterval(0.95).ClosedContains(uncertainties.X.Mean));
Assert.IsTrue(values.Y.PopulationStandardDeviation.ConfidenceInterval(0.95).ClosedContains(uncertainties.Y.Mean));
}
