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

KolmogorovSmirnovDistribution 
Creates a new KolmogorovSmirnov distribution.

Name  Description  

Entropy 
Gets the entropy for this distribution.
(Overrides UnivariateContinuousDistributionEntropy.)  
Mean 
Gets the mean for this distribution.
(Overrides UnivariateContinuousDistributionMean.)  
Median 
Gets the median for this distribution.
(Inherited from UnivariateContinuousDistribution.)  
Mode 
Not supported.
(Overrides UnivariateContinuousDistributionMode.)  
NumberOfSamples 
Gets the number of samples distribution parameter.
 
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.)  
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(Double) 
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.)  
ComplementaryDistributionFunction(Double, Double) 
Computes the Complementary Cumulative Distribution Function (1CDF)
for the KolmogorovSmirnov statistic's distribution.
 
CumulativeFunction 
Computes the Cumulative Distribution Function (CDF)
for the KolmogorovSmirnov statistic's distribution.
 
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.)  
Durbin 
Durbin's algorithm for computing P[Dn < d]
 
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) 
Not supported.
(Overrides UnivariateContinuousDistributionFit(Double, Double, IFittingOptions).)  
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 x.
(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.
(Inherited from UnivariateContinuousDistribution.)  
InnerLogProbabilityDensityFunction 
Gets the logprobability density function (pdf) for
this distribution evaluated at point x.
(Inherited from UnivariateContinuousDistribution.)  
InnerProbabilityDensityFunction 
Not supported.
(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.)  
MemberwiseClone  Creates a shallow copy of the current Object. (Inherited from Object.)  
OneSideDistributionFunction 
Computes the Upper Tail of the P[Dn >= x] distribution.
 
OneSideUpperTail 
Computes the Upper Tail of the P[Dn >= x] distribution.
 
PelzGood 
PelzGood algorithm for computing lowertail areas
of the KolmogorovSmirnov distribution.
 
Pomeranz 
Pomeranz algorithm.
 
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 class is based on the excellent paper and original Java code by Simard and L'Ecuyer (2010). Includes additional modifications for increased performance and readability, shared under the LGPL under permission of original authors.
L'Ecuyer and Simard partitioned the problem of evaluating the CDF using multiple approximation and asymptotic methods in order to achieve a best compromise between speed and precision. The distribution function of this class follows the same partitioning scheme as described by L'Ecuyer and Simard, which is described in the table below.
For n <= 140 and:  

1/n > x >= 11/n  Uses the RubenGambino formula. 
1/n < nx² < 0.754693  Uses the Durbin matrix algorithm. 
0.754693 <= nx² < 4  Uses the Pomeranz algorithm. 
4 <= nx² < 18  Uses the complementary distribution function. 
nx² >= 18  Returns the constant 1. 
For 140 < n <= 10^5  

nx² >= 18  Returns the constant 1. 
nx^(3/2) < 1.4  Durbin matrix algorithm. 
nx^(3/2) > 1.4  PelzGood asymptotic series. 
For n > 10^5  

nx² >= 18  Returns the constant 1. 
nx² < 18  PelzGood asymptotic series. 
References:
The following example shows how to build a KolmogorovSmirnov distribution for 42 samples and compute its main functions and characteristics:
// Create a KolmogorovSmirnov distribution with n = 42 var ks = new KolmogorovSmirnovDistribution(samples: 42); // Common measures double mean = ks.Mean; // 0.13404812830261556 double median = ks.Median; // 0.12393613519421857 double var = ks.Variance; // 0.019154717445778062 // Cumulative distribution functions double cdf = ks.DistributionFunction(x: 0.27); // 0.99659863602996079 double ccdf = ks.ComplementaryDistributionFunction(x: 0.27); // 0.0034013639700392062 double icdf = ks.InverseDistributionFunction(p: cdf); // 0.26999997446092017 // Hazard (failure rate) functions double chf = ks.CumulativeHazardFunction(x: 0.27); // 5.6835787601476619 // String representation string str = ks.ToString(); // "KS(x; n = 42)"