public static string TestAgainstStandardDistribution(IList <double> sortedListOfData, LinearBinning binning, INumericColumn colBinPosition, INumericColumn colBinCounts)
{
var stb = new StringBuilder();
var stat = new Calc.Regression.QuickStatistics();
foreach (var v in sortedListOfData)
{
stat.Add(v);
}
// Test the probability against the normal distribution
// First make a fit of the normal distribution to get mu and sigma
// guess of mu
double guessedMu = stat.Mean;
double guessedSigma = stat.SampleStandardDeviation;
/*
* Altaxo.Calc.Regression.Nonlinear.SimpleNonlinearFit fit = new Altaxo.Calc.Regression.Nonlinear.SimpleNonlinearFit(
* delegate (double[] indep, double[] p, double[] res)
* {
* // 3 Parameter: mu and sigma
* res[0] = Calc.Probability.NormalDistribution.PDF(indep[0], p[0], p[1]);
* },
* new double[] { guessedMu, guessedSigma },
* colBinPosition,
* colProbabilityDensity,
* 0, // Start (first point)
* binning.Count // point count
* );
*
* fit.Fit();
*
* guessedMu = fit.GetParameter(0);
* guessedSigma = fit.GetParameter(1);
*
*/
// Test hypothesis that we have a normal distribution
double chiSquare = 0;
int degreesOfFreedom = binning.NumberOfBins - 1 - 2; // -2 because we lost two degrees of freedom in the previous fitting
for (int nBinIndex = 0; nBinIndex < binning.NumberOfBins; ++nBinIndex)
{
var bin = binning.Bins[nBinIndex];
double lowerBound = bin.LowerBound;
double upperBound = bin.UpperBound;
var probability = Calc.Probability.NormalDistribution.CDF(upperBound, guessedMu, guessedSigma) - Calc.Probability.NormalDistribution.CDF(lowerBound, guessedMu, guessedSigma);
double n0 = probability * sortedListOfData.Count;
chiSquare += RMath.Pow2(n0 - colBinCounts[nBinIndex]) / n0;
}
double chiSquareThreshold = Calc.Probability.ChiSquareDistribution.Quantile(0.95, degreesOfFreedom);
if (chiSquare <= chiSquareThreshold)
{
stb.AppendFormat("The hypothesis that this is a normal distribution with mu={0} and sigma={1} can not be rejected. ChiSquare ({2}) is less than ChiSquare needed to reject hypothesis ({3})", guessedMu, guessedSigma, chiSquare, chiSquareThreshold);
}
else
{
stb.AppendFormat("The hypothesis that this is a normal distribution with mu={0} and sigma={1} must be rejected with a confidence of {2}%. ChiSquare ({3}) is greater than ChiSquare needed to reject hypothesis ({4})", guessedMu, guessedSigma, 100 * Altaxo.Calc.Probability.ChiSquareDistribution.CDF(chiSquare, degreesOfFreedom), chiSquare, chiSquareThreshold);
}
return(stb.ToString());
}
internal BinList(LinearBinning b)
{
_parent = b;
}