/// <summary>
/// Creates a new Anderson-Darling test.
/// </summary>
///
/// <param name="sample">The sample we would like to test as belonging to the <paramref name="hypothesizedDistribution"/>.</param>
/// <param name="hypothesizedDistribution">A fully specified distribution.</param>
///
public AndersonDarlingTest(double[] sample, IUnivariateDistribution <double> hypothesizedDistribution)
{
// Create the test statistic distribution
this.TheoreticalDistribution = hypothesizedDistribution;
if (hypothesizedDistribution is UniformContinuousDistribution)
{
StatisticDistribution = new AndersonDarlingDistribution(AndersonDarlingDistributionType.Uniform, sample.Length);
}
else if (hypothesizedDistribution is NormalDistribution)
{
StatisticDistribution = new AndersonDarlingDistribution(AndersonDarlingDistributionType.Normal, sample.Length);
}
else
{
Trace.WriteLine(String.Format("Unsupported distribution in AndersonDarling: {0}. P-values will not be computed, but test statistic may be useful.",
hypothesizedDistribution.ToString(), hypothesizedDistribution.GetType().ToString()));
}
// Create a copy of the samples to prevent altering the
// constructor's original arguments in the sorting step
double[] sortedSamples = sample.Sorted();
// Create the theoretical and empirical distributions
this.TheoreticalDistribution = hypothesizedDistribution;
this.Statistic = GetStatistic(sortedSamples, TheoreticalDistribution);
this.PValue = StatisticToPValue(Statistic);
}
/// <summary>
/// Vapnik Chervonenkis test.
/// </summary>
/// <param name="epsilon">The error we are willing to tolerate.</param>
/// <param name="delta">The error probability we are willing to tolerate.</param>
/// <param name="s">The samples to use for testing.</param>
/// <param name="dist">The distribution we are testing.</param>
public static void VapnikChervonenkisTest(double epsilon, double delta, IEnumerable <double> s, IUnivariateDistribution dist)
{
// Using VC-dimension, we can bound the probability of making an error when estimating empirical probability
// distributions. We are using Theorem 2.41 in "All Of Nonparametric Statistics".
// http://books.google.com/books?id=MRFlzQfRg7UC&lpg=PP1&dq=all%20of%20nonparametric%20statistics&pg=PA22#v=onepage&q=%22shatter%20coe%EF%AC%83cients%20do%20not%22&f=false .</para>
// For intervals on the real line the VC-dimension is 2.
double n = s.Count();
Assert.Greater(n, Math.Ceiling(32.0 * Math.Log(16.0 / delta) / epsilon / epsilon));
var histogram = new Histogram(s, NumberOfBuckets);
for (var i = 0; i < NumberOfBuckets; i++)
{
var p = dist.CumulativeDistribution(histogram[i].UpperBound) - dist.CumulativeDistribution(histogram[i].LowerBound);
var pe = histogram[i].Count / n;
Assert.Less(Math.Abs(p - pe), epsilon, dist.ToString());
}
}
/// <summary>
/// Vapnik Chervonenkis test.
/// </summary>
/// <param name="epsilon">The error we are willing to tolerate.</param>
/// <param name="delta">The error probability we are willing to tolerate.</param>
/// <param name="s">The samples to use for testing.</param>
/// <param name="dist">The distribution we are testing.</param>
public static void VapnikChervonenkisTest(double epsilon, double delta, IEnumerable<double> s, IUnivariateDistribution dist)
{
// Using VC-dimension, we can bound the probability of making an error when estimating empirical probability
// distributions. We are using Theorem 2.41 in "All Of Nonparametric Statistics".
// http://books.google.com/books?id=MRFlzQfRg7UC&lpg=PP1&dq=all%20of%20nonparametric%20statistics&pg=PA22#v=onepage&q=%22shatter%20coe%EF%AC%83cients%20do%20not%22&f=false .</para>
// For intervals on the real line the VC-dimension is 2.
double n = s.Count();
Assert.Greater(n, Math.Ceiling(32.0 * Math.Log(16.0 / delta) / epsilon / epsilon));
var histogram = new Histogram(s, NumberOfBuckets);
for (var i = 0; i < NumberOfBuckets; i++)
{
var p = dist.CumulativeDistribution(histogram[i].UpperBound) - dist.CumulativeDistribution(histogram[i].LowerBound);
var pe = histogram[i].Count / n;
Assert.Less(Math.Abs(p - pe), epsilon, dist.ToString());
}
}
private PlotModel createBaseModel(DoubleRange?range, string title, double[] x, double[] y, bool discrete)
{
var plotModel = new PlotModel();
plotModel.Series.Clear();
plotModel.Axes.Clear();
double ymin = y.FirstOrDefault(a => !Double.IsNaN(a) && !Double.IsInfinity(a));
double ymax = ymin;
for (int i = 0; i < y.Length; i++)
{
if (Double.IsNaN(y[i]) || Double.IsInfinity(y[i]))
{
continue;
}
if (y[i] > ymax)
{
ymax = y[i];
}
if (y[i] < ymin)
{
ymin = y[i];
}
}
double maxGrace = ymax * 0.1;
double minGrace = ymin * 0.1;
if (!discrete)
{
var xAxis = new OxyPlot.Axes.LinearAxis()
{
Position = AxisPosition.Bottom,
Minimum = range.Value.Min,
Maximum = range.Value.Max,
Key = "xAxis",
MajorGridlineStyle = LineStyle.Solid,
MinorGridlineStyle = LineStyle.Dot,
IntervalLength = 80
};
var yAxis = new LinearAxis()
{
Position = AxisPosition.Left,
Minimum = ymin - minGrace,
Maximum = ymax + maxGrace,
Key = "yAxis",
MajorGridlineStyle = LineStyle.Solid,
MinorGridlineStyle = LineStyle.Dot,
Title = title
};
plotModel.Axes.Add(xAxis);
plotModel.Axes.Add(yAxis);
var lineSeries = new LineSeries
{
YAxisKey = yAxis.Key,
XAxisKey = xAxis.Key,
StrokeThickness = 2,
MarkerSize = 3,
MarkerStroke = OxyColor.FromRgb(0, 0, 0),
MarkerType = MarkerType.None,
Smooth = true,
};
for (int i = 0; i < x.Length; i++)
{
if (Double.IsNaN(y[i]) || Double.IsInfinity(y[i]))
{
continue;
}
lineSeries.Points.Add(new DataPoint(x[i], y[i]));
}
plotModel.Series.Add(lineSeries);
}
else
{
var xAxis = new OxyPlot.Axes.CategoryAxis()
{
Position = AxisPosition.Bottom,
Key = "xAxis",
MajorGridlineStyle = LineStyle.Solid,
MinorGridlineStyle = LineStyle.Dot,
};
var yAxis = new LinearAxis()
{
Position = AxisPosition.Left,
Minimum = ymin - minGrace,
Maximum = ymax + maxGrace,
Key = "yAxis",
MajorGridlineStyle = LineStyle.Solid,
MinorGridlineStyle = LineStyle.Dot,
Title = title
};
plotModel.Axes.Add(xAxis);
plotModel.Axes.Add(yAxis);
var boxSeries = new ColumnSeries
{
YAxisKey = yAxis.Key,
XAxisKey = xAxis.Key,
StrokeThickness = 2,
ColumnWidth = 1,
};
for (int i = 0; i < x.Length; i++)
{
xAxis.Labels.Add(x[i].ToString("G2"));
var item = new ColumnItem(y[i]);
boxSeries.Items.Add(item);
}
plotModel.Series.Add(boxSeries);
}
var formattable = instance as IFormattable;
if (formattable != null)
{
plotModel.Title = formattable.ToString("G3", CultureInfo.CurrentUICulture);
}
else
{
plotModel.Title = instance.ToString();
}
plotModel.TitlePadding = 2;
plotModel.TitleFontSize = 15;
plotModel.TitleFontWeight = 1;
plotModel.TitlePadding = 2;
return(plotModel);
}
