# SuanShu, a Java numerical and statistical library

com.numericalmethod.suanshu.stats.test.distribution.kolmogorov

## Class KolmogorovDistribution

• java.lang.Object
• com.numericalmethod.suanshu.stats.test.distribution.kolmogorov.KolmogorovDistribution
• All Implemented Interfaces:
ProbabilityDistribution

public class KolmogorovDistribution
extends Object
implements ProbabilityDistribution
The Kolmogorov distribution is the distribution of the Kolmogorov-Smirnov statistic. The statistic is defined as the supremum of the absolute difference between the empirical and reference distributions.
See Also:
• "George Marsaglia, Wai Wan Tsang, Jingbo Wang, "Evaluating Kolmogorov's distribution," Journal of Statistical Software, 8/18."
• "J. H. Drew, A. G. Glen, and L. M. Leemis, "Computing the cumulative distribution function of the Kolmogorov-Smirnov statistic," Computational Statistics and Data Analysis 34 (2000) 1-15."
• Wikipedia: Kolmogorov distribution
• ### Constructor Summary

Constructors
Constructor and Description
KolmogorovDistribution(int n)
Construct a Kolmogorov distribution for a sample size n.
KolmogorovDistribution(int n, int bigN, boolean rightTailApproximation)
Construct a Kolmogorov distribution for a sample size n.
• ### Method Summary

All Methods
Modifier and Type Method and Description
static double asymptoticCDF(double x)
This is the asymptotic distribution of the Kolmogorov distribution.
double cdf(double d)
Gets the cumulative probability F(x) = Pr(X ≤ x).
double density(double x)
Deprecated.
double entropy()
Deprecated.
double kurtosis()
Deprecated.
double mean()
Deprecated.
double median()
Deprecated.
double moment(double x)
Deprecated.
double quantile(double u)
Deprecated.
double skew()
Deprecated.
double variance()
Deprecated.
• ### Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
• ### Constructor Detail

• #### KolmogorovDistribution

public KolmogorovDistribution(int n,
int bigN,
boolean rightTailApproximation)
Construct a Kolmogorov distribution for a sample size n.
Parameters:
n - the number of observations
bigN - the threshold to use the asymptotic distribution when n > bigN
rightTailApproximation - true if we use the right tail approximation; the accuracy is up to 7 digits
• #### KolmogorovDistribution

public KolmogorovDistribution(int n)
Construct a Kolmogorov distribution for a sample size n. We use the asymptotic distribution when n > 16000. We use an approximation for the right tail.
Parameters:
n - the number of observations
• ### Method Detail

• #### mean

@Deprecated
public double mean()
Deprecated.
Description copied from interface: ProbabilityDistribution
Gets the mean of this distribution.
Specified by:
mean in interface ProbabilityDistribution
Returns:
the mean
See Also:
Wikipedia: Expected value
• #### median

@Deprecated
public double median()
Deprecated.
Description copied from interface: ProbabilityDistribution
Gets the median of this distribution.
Specified by:
median in interface ProbabilityDistribution
Returns:
the median
See Also:
Wikipedia: Median
• #### variance

@Deprecated
public double variance()
Deprecated.
Description copied from interface: ProbabilityDistribution
Gets the variance of this distribution.
Specified by:
variance in interface ProbabilityDistribution
Returns:
the variance
See Also:
Wikipedia: Variance
• #### skew

@Deprecated
public double skew()
Deprecated.
Description copied from interface: ProbabilityDistribution
Gets the skewness of this distribution.
Specified by:
skew in interface ProbabilityDistribution
Returns:
the skewness
See Also:
Wikipedia: Skewness
• #### kurtosis

@Deprecated
public double kurtosis()
Deprecated.
Description copied from interface: ProbabilityDistribution
Gets the excess kurtosis of this distribution.
Specified by:
kurtosis in interface ProbabilityDistribution
Returns:
the excess kurtosis
See Also:
Wikipedia: Kurtosis
• #### entropy

@Deprecated
public double entropy()
Deprecated.
Description copied from interface: ProbabilityDistribution
Gets the entropy of this distribution.
Specified by:
entropy in interface ProbabilityDistribution
Returns:
the entropy
See Also:
Wikipedia: Entropy (information theory)
• #### cdf

public double cdf(double d)
Description copied from interface: ProbabilityDistribution
Gets the cumulative probability F(x) = Pr(X ≤ x).
Specified by:
cdf in interface ProbabilityDistribution
Parameters:
d - x
Returns:
F(x) = Pr(X ≤ x)
See Also:
Wikipedia: Cumulative distribution function
• #### asymptoticCDF

public static double asymptoticCDF(double x)
This is the asymptotic distribution of the Kolmogorov distribution.
Parameters:
x - a critical value
Returns:
F(x)
See Also:
Wikipedia: Kolmogorov distribution
• #### quantile

@Deprecated
public double quantile(double u)
Deprecated.
Description copied from interface: ProbabilityDistribution
Gets the quantile, the inverse of the cumulative distribution function. It is the value below which random draws from the distribution would fall u×100 percent of the time.

F-1(u) = x, such that
Pr(X ≤ x) = u

This may not always exist.
Specified by:
quantile in interface ProbabilityDistribution
Parameters:
u - u, a quantile
Returns:
F-1(u)
See Also:
Wikipedia: Quantile function
• #### density

@Deprecated
public double density(double x)
Deprecated.
Description copied from interface: ProbabilityDistribution
The density function, which, if exists, is the derivative of F. It describes the density of probability at each point in the sample space.
f(x) = dF(X) / dx
This may not always exist.

For the discrete cases, this is the probability mass function. It gives the probability that a discrete random variable is exactly equal to some value.

Specified by:
density in interface ProbabilityDistribution
Parameters:
x - x
Returns:
f(x)
See Also:
• #### moment

@Deprecated
public double moment(double x)
Deprecated.
Description copied from interface: ProbabilityDistribution
The moment generating function is the expected value of etX. That is,
E(etX)
This may not always exist.
Specified by:
moment in interface ProbabilityDistribution
Parameters:
x - t
Returns:
E(exp(tX))
See Also:
Wikipedia: Moment-generating function

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