WilcoxonDistribution Class

[SerializableAttribute]
public class WilcoxonDistribution : UnivariateContinuousDistribution

<SerializableAttribute>
Public Class WilcoxonDistribution
	Inherits UnivariateContinuousDistribution

// Compute some rank statistics (see other examples below)
double[] ranks = { 1, 2, 3, 4, 5.5, 5.5, 7, 8, 9, 10, 11, 12 };

// Create a new Wilcoxon's W distribution
WilcoxonDistribution W = new WilcoxonDistribution(ranks);

// Common measures
double mean = W.Mean;     // 39.0
double median = W.Median; // 38.5
double var = W.Variance;  // 162.5

// Probability density functions
double pdf = W.ProbabilityDensityFunction(w: 42);     // 0.38418508862319295
double lpdf = W.LogProbabilityDensityFunction(w: 42); // 0.38418508862319295

// Cumulative distribution functions
double cdf = W.DistributionFunction(w: 42);               // 0.60817384423279575
double ccdf = W.ComplementaryDistributionFunction(x: 42); // 0.39182615576720425

// Quantile function
double icdf = W.InverseDistributionFunction(p: cdf); // 42

// Hazard (failure rate) functions
double hf = W.HazardFunction(x: 42);            // 0.98049883339449373
double chf = W.CumulativeHazardFunction(x: 42); // 0.936937017743799

// String representation
string str = W.ToString(); // "W+(x; R)"

// Suppose we have computed a vector of differences between
// samples and an hypothesized value (as in Wilcoxon's test).

double[] differences = ... // differences between samples and an hypothesized median

// Compute the ranks of the absolute differences and their sign
double[] ranks = Measures.Rank(differences.Abs());
int[] signs    = Accord.Math.Matrix.Sign(differences).ToInt32();

// Compute the W+ statistics from the signed ranks
double W = WilcoxonDistribution.WPositive(Signs, ranks);