public void InternetSampleDownload()
{
FrameTable table = DownloadFrameTable(new Uri("https://raw.githubusercontent.com/Dataweekends/zero_to_deep_learning_udemy/master/data/weight-height.csv"));
FrameView view = table.WhereNotNull();
view.AddComputedColumn("Bmi", (FrameRow r) => {
double h = (double)r["Height"];
double w = (double)r["Weight"];
return(w / (h * h));
});
FrameView males = view.Where("Gender", (string s) => (s == "Male"));
FrameView females = view.Where("Gender", (string s) => (s == "Female"));
SummaryStatistics maleSummary = new SummaryStatistics(males["Height"].As <double>());
SummaryStatistics femaleSummary = new SummaryStatistics(females["Height"].As <double>());
TestResult allNormal = view["Height"].As <double>().ShapiroFranciaTest();
TestResult maleNormal = males["Height"].As <double>().ShapiroFranciaTest();
TestResult femaleNormal = females["Height"].As <double>().ShapiroFranciaTest();
TestResult tTest = Univariate.StudentTTest(males["Height"].As <double>(), females["Height"].As <double>());
TestResult mwTest = Univariate.MannWhitneyTest(males["Height"].As <double>(), females["Height"].As <double>());
LinearRegressionResult result0 = males["Weight"].As <double>().LinearRegression(males["Height"].As <double>());
PolynomialRegressionResult result1 = males["Height"].As <double>().PolynomialRegression(males["Weight"].As <double>(), 1);
PolynomialRegressionResult result2 = males["Height"].As <double>().PolynomialRegression(males["Weight"].As <double>(), 2);
PolynomialRegressionResult result3 = males["Height"].As <double>().PolynomialRegression(males["Weight"].As <double>(), 3);
//MultiLinearRegressionResult multi = view["Weight"].As<double>().MultiLinearRegression(view["Height"].As<double>(), view["Gender"].As<string>().Select(s => (s == "Male") ? 1.0 : 0.0).ToList());
}
//function to calc Mann-Whitney statistics
private double[] calcMWStats()
{
double[] stats = new double[8]; //to store final stats
List <double> stoichsG1 = new List <double>(); //double[(this.PeptideStoichiometriesGroupOne.Count()]; //list to store distribution of group one stoichiometries
List <double> stoichsG2 = new List <double>(); //double[(this.PeptideStoichiometriesGroupTwo.Count()]; //list to store distribution of group two stoichiometries
foreach (Stoichiometry S1 in (this.PeptideStoichiometriesGroupOne))
{
stoichsG1.Add(S1.StoichiometryVal);
}
foreach (Stoichiometry S2 in (this.PeptideStoichiometriesGroupTwo))
{
stoichsG2.Add(S2.StoichiometryVal);
}
//calc stats
TestResult mw = Univariate.MannWhitneyTest(stoichsG1, stoichsG2);
stats[0] = mw.Statistic.Value;
stats[1] = mw.Probability;
//find medians, mins maxs
stats[2] = stoichsG1.Median();
stats[4] = stoichsG1.Min();
stats[6] = stoichsG1.Max();
stats[3] = stoichsG2.Median();
stats[5] = stoichsG2.Min();
stats[7] = stoichsG2.Max();
return(stats);
}
private static void CompareSamples()
{
List <double> a = new List <double>()
{
130.0, 140.0, 150.0, 150.0, 160.0, 190.0
};
List <double> b = new List <double>()
{
120.0, 150.0, 180.0, 170.0, 185.0, 175.0, 190.0, 200.0
};
TestResult student = Univariate.StudentTTest(a, b);
Console.WriteLine($"{student.Statistic.Name} = {student.Statistic.Value}");
Console.WriteLine($"{student.Type} P = {student.Probability}");
student.Type = TestType.LeftTailed;
Console.WriteLine($"{student.Type} P = {student.Probability}");
TestResult mannWhitney = Univariate.MannWhitneyTest(a, b);
Console.WriteLine($"{mannWhitney.Statistic.Name} = {mannWhitney.Statistic.Value}");
Console.WriteLine($"{mannWhitney.Type} P = {mannWhitney.Probability}");
TestResult kolmogorov = Univariate.KolmogorovSmirnovTest(a, b);
Console.WriteLine($"{kolmogorov.Statistic.Name} = {kolmogorov.Statistic.Value}");
Console.WriteLine($"{kolmogorov.Type} P = {kolmogorov.Probability}");
}
public void UnivariateTest()
{
var univariate = new Univariate(1, 6, 7);
Assert.AreEqual(-1.58, univariate.FirstAnswer, 0.01);
Assert.AreEqual(-4.41, univariate.SecondAnswer, 0.01);
}
/// <summary>
/// Computes the exponential distribution that best fits the given sample.
/// </summary>
/// <param name="sample">The sample to fit.</param>
/// <returns>The best fit parameter.</returns>
/// <remarks>
/// <para>The returned fit parameter is μ (the <see cref="Mean"/>).
/// This is the same parameter that is required by the <see cref="ExponentialDistribution(double)"/> constructor to
/// specify a new exponential distribution.</para>
/// </remarks>
/// <exception cref="ArgumentNullException"><paramref name="sample"/> is null.</exception>
/// <exception cref="InsufficientDataException"><paramref name="sample"/> contains fewer than two values.</exception>
/// <exception cref="InvalidOperationException"><paramref name="sample"/> contains non-positive values.</exception>
public static ExponentialFitResult FitToSample(Sample sample)
{
if (sample == null)
{
throw new ArgumentNullException(nameof(sample));
}
return(Univariate.FitToExponential(sample.data));
}
/// <summary>
/// Fits a Rayleigh distribution to a sample.
/// </summary>
/// <param name="sample">The sample to fit, which must have at least 2 values.</param>
/// <returns>The fit result. The only parameter is the scale parameter.</returns>
public static RayleighFitResult FitToSample(Sample sample)
{
if (sample == null)
{
throw new ArgumentNullException(nameof(sample));
}
return(Univariate.FitToRayleigh(sample.data));
}
public void TwoSampleKolmogorovNullDistributionTest()
{
Random rng = new Random(4);
ContinuousDistribution population = new ExponentialDistribution();
int[] sizes = new int[] { 23, 30, 175 };
foreach (int na in sizes)
{
foreach (int nb in sizes)
{
Sample d = new Sample();
ContinuousDistribution nullDistribution = null;
for (int i = 0; i < 128; i++)
{
List <double> a = TestUtilities.CreateDataSample(rng, population, na).ToList();
List <double> b = TestUtilities.CreateDataSample(rng, population, nb).ToList();
TestResult r = Univariate.KolmogorovSmirnovTest(a, b);
d.Add(r.Statistic.Value);
nullDistribution = r.Statistic.Distribution;
}
// Only do full KS test if the number of bins is larger than the sample size, otherwise we are going to fail
// because the KS test detects the granularity of the distribution.
TestResult mr = d.KolmogorovSmirnovTest(nullDistribution);
if (AdvancedIntegerMath.LCM(na, nb) > d.Count)
{
Assert.IsTrue(mr.Probability > 0.01);
}
// But always test that mean and standard deviation are as expected
Assert.IsTrue(d.PopulationMean.ConfidenceInterval(0.99).ClosedContains(nullDistribution.Mean));
Assert.IsTrue(d.PopulationStandardDeviation.ConfidenceInterval(0.99).ClosedContains(nullDistribution.StandardDeviation));
// This test is actually a bit sensitive, probably because the discrete-ness of the underlying distribution
// and the inaccuracy of the asymptotic approximation for intermediate sample size make strict comparisons iffy.
}
}
}
public static void AnalyzingData()
{
FrameTable table;
Uri url = new Uri("https://raw.githubusercontent.com/dcwuser/metanumerics/master/Examples/Data/example.csv");
WebRequest request = WebRequest.Create(url);
using (WebResponse response = request.GetResponse()) {
using (StreamReader reader = new StreamReader(response.GetResponseStream())) {
table = FrameTable.FromCsv(reader);
}
}
FrameView view = table.WhereNotNull();
// Get the column with (zero-based) index 4.
FrameColumn column4 = view.Columns[4];
// Get the column named "Height".
FrameColumn heightsColumn = view.Columns["Height"];
// Even easier way to get the column named "Height".
FrameColumn alsoHeightsColumn = view["Height"];
IReadOnlyList <double> heights = view["Height"].As <double>();
SummaryStatistics summary = new SummaryStatistics(view["Height"].As <double>());
Console.WriteLine($"Count = {summary.Count}");
Console.WriteLine($"Mean = {summary.Mean}");
Console.WriteLine($"Standard Deviation = {summary.StandardDeviation}");
Console.WriteLine($"Skewness = {summary.Skewness}");
Console.WriteLine($"Estimated population mean = {summary.PopulationMean}");
Console.WriteLine($"Estimated population standard deviation = {summary.PopulationStandardDeviation}");
IReadOnlyList <double> maleHeights =
view.Where <string>("Sex", s => s == "M").Columns["Height"].As <double>();
IReadOnlyList <double> femaleHeights =
view.Where <string>("Sex", s => s == "F").Columns["Height"].As <double>();
TestResult test = Univariate.StudentTTest(maleHeights, femaleHeights);
Console.WriteLine($"{test.Statistic.Name} = {test.Statistic.Value}");
Console.WriteLine($"P = {test.Probability}");
TestResult maleHeightNormality = maleHeights.ShapiroFranciaTest();
TestResult totalHeightNormality = view["Height"].As <double>().ShapiroFranciaTest();
TestResult heightCompatibility = Univariate.KolmogorovSmirnovTest(maleHeights, femaleHeights);
LinearRegressionResult fit =
view["Weight"].As <double>().LinearRegression(view["Height"].As <double>());
Console.WriteLine($"Model weight = ({fit.Slope}) * height + ({fit.Intercept}).");
Console.WriteLine($"Model explains {fit.RSquared * 100.0}% of variation.");
ContingencyTable <string, bool> contingency =
Bivariate.Crosstabs(view["Sex"].As <string>(), view["Result"].As <bool>());
Console.WriteLine($"Male incidence: {contingency.ProbabilityOfColumnConditionalOnRow(true, "M")}");
Console.WriteLine($"Female incidence: {contingency.ProbabilityOfColumnConditionalOnRow(true, "F")}");
Console.WriteLine($"Log odds ratio = {contingency.Binary.LogOddsRatio}");
view.AddComputedColumn("Bmi", r => ((double)r["Weight"]) / MoreMath.Sqr((double)r["Height"] / 100.0));
view.AddComputedColumn("Age", r => (DateTime.Now - (DateTime)r["Birthdate"]).TotalDays / 365.24);
MultiLinearLogisticRegressionResult result =
view["Result"].As <bool>().MultiLinearLogisticRegression(
view["Bmi"].As <double>(),
view["Sex"].As <string, double>(s => s == "M" ? 1.0 : 0.0)
);
foreach (Parameter parameter in result.Parameters)
{
Console.WriteLine($"{parameter.Name} = {parameter.Estimate}");
}
TestResult spearman = Bivariate.SpearmanRhoTest(view["Age"].As <double>(), view["Result"].As <double>());
Console.WriteLine($"{spearman.Statistic.Name} = {spearman.Statistic.Value} P = {spearman.Probability}");
}