MannWhitneyDistribution Class 
Namespace: Accord.Statistics.Distributions.Univariate
[SerializableAttribute] public class MannWhitneyDistribution : UnivariateContinuousDistribution
The MannWhitneyDistribution type exposes the following members.
Name  Description  

MannWhitneyDistribution(Int32, Int32) 
Constructs a MannWhitney's Ustatistic distribution.
 
MannWhitneyDistribution(Double, Double, NullableBoolean) 
Constructs a MannWhitney's Ustatistic distribution.
 
MannWhitneyDistribution(Double, Int32, Int32, NullableBoolean) 
Constructs a MannWhitney's Ustatistic distribution.

Name  Description  

Correction 
Gets or sets the continuity correction
to be applied when using the Normal approximation to this distribution.
 
Entropy 
This method is not supported.
(Overrides UnivariateContinuousDistributionEntropy.)  
Exact 
Gets whether this distribution computes the exact probabilities
(by searching all possible rank combinations) or gives fast
approximations.
 
Mean 
Gets the mean for this distribution.
(Overrides UnivariateContinuousDistributionMean.)  
Median 
Gets the median for this distribution.
(Inherited from UnivariateContinuousDistribution.)  
Mode 
This method is not supported.
(Overrides UnivariateContinuousDistributionMode.)  
NumberOfSamples1 
Gets the number of observations in the first sample.
 
NumberOfSamples2 
Gets the number of observations in the second sample.
 
Quartiles 
Gets the Quartiles for this distribution.
(Inherited from UnivariateContinuousDistribution.)  
StandardDeviation 
Gets the Standard Deviation (the square root of
the variance) for the current distribution.
(Inherited from UnivariateContinuousDistribution.)  
Support 
Gets the support interval for this distribution.
(Overrides UnivariateContinuousDistributionSupport.)  
Table 
Gets the statistic values for all possible combinations
of ranks. This is used to compute the exact distribution.
 
Variance 
Gets the variance for this distribution.
(Overrides UnivariateContinuousDistributionVariance.) 
Name  Description  

Clone 
Creates a new object that is a copy of the current instance.
(Overrides DistributionBaseClone.)  
ComplementaryDistributionFunction 
Gets the complementary cumulative distribution function
(ccdf) for this distribution evaluated at point x.
This function is also known as the Survival function.
(Inherited from UnivariateContinuousDistribution.)  
CumulativeHazardFunction 
Gets the cumulative hazard function for this
distribution evaluated at point x.
(Inherited from UnivariateContinuousDistribution.)  
DistributionFunction(Double) 
Gets the cumulative distribution function (cdf) for
this distribution evaluated at point x.
(Inherited from UnivariateContinuousDistribution.)  
DistributionFunction(Double, Double) 
Gets the cumulative distribution function (cdf) for this
distribution in the semiclosed interval (a; b] given as
P(a < X ≤ b).
(Inherited from UnivariateContinuousDistribution.)  
Equals  Determines whether the specified object is equal to the current object. (Inherited from Object.)  
Finalize  Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object.)  
Fit(Double) 
Fits the underlying distribution to a given set of observations.
(Inherited from UnivariateContinuousDistribution.)  
Fit(Double, IFittingOptions) 
Fits the underlying distribution to a given set of observations.
(Inherited from UnivariateContinuousDistribution.)  
Fit(Double, Double) 
Fits the underlying distribution to a given set of observations.
(Inherited from UnivariateContinuousDistribution.)  
Fit(Double, Int32) 
Fits the underlying distribution to a given set of observations.
(Inherited from UnivariateContinuousDistribution.)  
Fit(Double, Double, IFittingOptions) 
Fits the underlying distribution to a given set of observations.
(Inherited from UnivariateContinuousDistribution.)  
Fit(Double, Int32, IFittingOptions) 
Fits the underlying distribution to a given set of observations.
(Inherited from UnivariateContinuousDistribution.)  
Generate 
Generates a random observation from the current distribution.
(Inherited from UnivariateContinuousDistribution.)  
Generate(Int32) 
Generates a random vector of observations from the current distribution.
(Inherited from UnivariateContinuousDistribution.)  
Generate(Random) 
Generates a random observation from the current distribution.
(Inherited from UnivariateContinuousDistribution.)  
Generate(Int32, Double) 
Generates a random vector of observations from the current distribution.
(Inherited from UnivariateContinuousDistribution.)  
Generate(Int32, Random) 
Generates a random vector of observations from the current distribution.
(Inherited from UnivariateContinuousDistribution.)  
Generate(Int32, Double, Random) 
Generates a random vector of observations from the current distribution.
(Inherited from UnivariateContinuousDistribution.)  
GetHashCode  Serves as the default hash function. (Inherited from Object.)  
GetRange 
Gets the distribution range within a given percentile.
(Inherited from UnivariateContinuousDistribution.)  
GetType  Gets the Type of the current instance. (Inherited from Object.)  
HazardFunction 
Gets the hazard function, also known as the failure rate or
the conditional failure density function for this distribution
evaluated at point x.
(Inherited from UnivariateContinuousDistribution.)  
InnerComplementaryDistributionFunction 
Gets the complementary cumulative distribution function
(ccdf) for this distribution evaluated at point x.
This function is also known as the Survival function.
(Overrides UnivariateContinuousDistributionInnerComplementaryDistributionFunction(Double).)  
InnerDistributionFunction 
Gets the cumulative distribution function (cdf) for
this distribution evaluated at point k.
(Overrides UnivariateContinuousDistributionInnerDistributionFunction(Double).)  
InnerInverseDistributionFunction 
Gets the inverse of the cumulative distribution function (icdf) for
this distribution evaluated at probability p. This function
is also known as the Quantile function.
(Overrides UnivariateContinuousDistributionInnerInverseDistributionFunction(Double).)  
InnerLogProbabilityDensityFunction 
Gets the logprobability density function (pdf) for
this distribution evaluated at point x.
(Overrides UnivariateContinuousDistributionInnerLogProbabilityDensityFunction(Double).)  
InnerProbabilityDensityFunction 
Gets the probability density function (pdf) for
this distribution evaluated at point u.
(Overrides UnivariateContinuousDistributionInnerProbabilityDensityFunction(Double).)  
InverseDistributionFunction 
Gets the inverse of the cumulative distribution function (icdf) for
this distribution evaluated at probability p. This function
is also known as the Quantile function.
(Inherited from UnivariateContinuousDistribution.)  
LogCumulativeHazardFunction 
Gets the log of the cumulative hazard function for this
distribution evaluated at point x.
(Inherited from UnivariateContinuousDistribution.)  
LogProbabilityDensityFunction 
Gets the logprobability density function (pdf) for
this distribution evaluated at point x.
(Inherited from UnivariateContinuousDistribution.)  
MannWhitneyU 
Gets the MannWhitney's U statistic for the first sample.
 
MemberwiseClone  Creates a shallow copy of the current Object. (Inherited from Object.)  
ProbabilityDensityFunction 
Gets the probability density function (pdf) for
this distribution evaluated at point x.
(Inherited from UnivariateContinuousDistribution.)  
QuantileDensityFunction 
Gets the first derivative of the
inverse distribution function (icdf) for this distribution evaluated
at probability p.
(Inherited from UnivariateContinuousDistribution.)  
ToString 
Returns a String that represents this instance.
(Inherited from DistributionBase.)  
ToString(IFormatProvider) 
Returns a String that represents this instance.
(Inherited from DistributionBase.)  
ToString(String) 
Returns a String that represents this instance.
(Inherited from DistributionBase.)  
ToString(String, IFormatProvider) 
Returns a String that represents this instance.
(Overrides DistributionBaseToString(String, IFormatProvider).) 
Name  Description  

HasMethod 
Checks whether an object implements a method with the given name.
(Defined by ExtensionMethods.)  
IsEqual 
Compares two objects for equality, performing an elementwise
comparison if the elements are vectors or matrices.
(Defined by Matrix.)  
To(Type)  Overloaded.
Converts an object into another type, irrespective of whether
the conversion can be done at compile time or not. This can be
used to convert generic types to numeric types during runtime.
(Defined by ExtensionMethods.)  
ToT  Overloaded.
Converts an object into another type, irrespective of whether
the conversion can be done at compile time or not. This can be
used to convert generic types to numeric types during runtime.
(Defined by ExtensionMethods.) 
This is the distribution for MannWhitney's U statistic used in MannWhitneyWilcoxonTest. This distribution is based on sample Rank(Double, Boolean, Boolean) statistics.
This is the distribution for the first sample statistic, U1. Some textbooks (and statistical packages) use alternate definitions for U, which should be compared with the appropriate statistic tables or alternate distributions.
// Consider the following rank statistics double[] ranks = { 1, 2, 3, 4, 5 }; // Create a new MannWhitney U's distribution with n1 = 2 and n2 = 3 var mannWhitney = new MannWhitneyDistribution(ranks, n1: 2, n2: 3); // Common measures double mean = mannWhitney.Mean; // 2.7870954605658511 double median = mannWhitney.Median; // 1.5219615583481305 double var = mannWhitney.Variance; // 18.28163603621158 // Cumulative distribution functions double cdf = mannWhitney.DistributionFunction(x: 4); // 0.6 double ccdf = mannWhitney.ComplementaryDistributionFunction(x: 4); // 0.4 double icdf = mannWhitney.InverseDistributionFunction(p: cdf); // 3.6666666666666661 // Probability density functions double pdf = mannWhitney.ProbabilityDensityFunction(x: 4); // 0.2 double lpdf = mannWhitney.LogProbabilityDensityFunction(x: 4); // 1.6094379124341005 // Hazard (failure rate) functions double hf = mannWhitney.HazardFunction(x: 4); // 0.5 double chf = mannWhitney.CumulativeHazardFunction(x: 4); // 0.916290731874155 // String representation string str = mannWhitney.ToString(); // MannWhitney(u; n1 = 2, n2 = 3)