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

Class KolmogorovDistribution

java.lang.Object

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

All Implemented Interfaces:

ProbabilityDistribution, java.io.Serializable

public class KolmogorovDistribution
extends java.lang.Object
implements ProbabilityDistribution

KolmogorovDistribution distribution is the distribution of the KolmogorovDistribution–Smirnov statistic. The statistic is defined as the supremum of the absolute difference between the empirical and reference distributions. To compute the cdf of the KolmogorovDistribution distribution, we implement the algorithm published in

 Evaluating KolmogorovDistribution's distribution
 by
 George Marsaglia, Wai Wan Tsang & Jingbo Wang (2003)
 Journal of Statistical Software, 8/18.
 

This part is not done yet. To compute the moments, we might use

 Computing the cumulative distribution function of the KolmogorovDistribution-Smirnov statistic
 Drew, J.H., Glen, A.G. and Leemis, L.M.
 Computational Statistics and Data Analysis 34 (2000) 1-15.
 

See Also:

• Wikipedia: KolmogorovDistribution distribution
• "George Marsaglia, Wai Wan Tsang & Jingbo Wang. "Evaluating KolmogorovDistribution's distribution," Journal of Statistical Software, 8/18."
• "Drew, J.H., Glen, A.G. and Leemis, L.M. "Computing the cumulative distribution function of the KolmogorovDistribution-Smirnov statistic," Computational Statistics and Data Analysis 34 (2000) 1-15."

, Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
int	bigN the big N for which n > bigN we use the asymptotic distribution
int	n the number of observations
boolean	rightTailApproximation true if we use approximation for the right tail to speed up computation; up to 7 digit of accuracy

Constructor Summary

Constructors

Constructor and Description
KolmogorovDistribution(int n) Construct a KolmogorovDistribution distribution for a sample size n.
KolmogorovDistribution(int n, int bigN, boolean rightTailApproximation) Construct a KolmogorovDistribution distribution for a sample size n.

Method Summary

Modifier and Type	Method and Description
static double	asymptoticCDF(double x) the asymptotic distribution of the KolmogorovDistribution distribution
double	cdf(double d) Get the cumulative probability F(x) = Pr(X ≤ x).
double	density(double x) Deprecated. Not supported yet.
double	entropy() Deprecated. Not supported yet.
double	kurtosis() Deprecated. Not supported yet.
double	mean() Deprecated. Not supported yet.
double	median() Deprecated. Not supported yet.
double	moment(double x) Deprecated. Not supported yet.
double	quantile(double u) Deprecated. Not supported yet.
double	skew() Deprecated. Not supported yet.
double	variance() Deprecated. Not supported yet.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

n

public final int n

the number of observations

bigN

public final int bigN

the big N for which n > bigN we use the asymptotic distribution

rightTailApproximation

public final boolean rightTailApproximation

true if we use approximation for the right tail to speed up computation; up to 7 digit of accuracy

Constructor Detail

KolmogorovDistribution

public KolmogorovDistribution(int n,
                              int bigN,
                              boolean rightTailApproximation)

Construct a KolmogorovDistribution distribution for a sample size n.

Parameters:

n - the number of observations

bigN - we use asymptotic distribution for n > bigN

rightTailApproximation - true if we use the right tail approximation

KolmogorovDistribution

public KolmogorovDistribution(int n)

Construct a KolmogorovDistribution distribution for a sample size n. We use the asymptotic distribution for n > 16000. We use an approximation for the right tail.

Parameters:

n - the number of observation

Method Detail

mean

@Deprecated
public double mean()

Deprecated. Not supported yet.

Description copied from interface: ProbabilityDistribution

Get 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. Not supported yet.

Description copied from interface: ProbabilityDistribution

Get the median of this distribution.

Specified by:

median in interface ProbabilityDistribution

Returns:

the median

See Also:

Wikipedia: Median

variance

@Deprecated
public double variance()

Deprecated. Not supported yet.

Description copied from interface: ProbabilityDistribution

Get the variance of this distribution.

Specified by:

variance in interface ProbabilityDistribution

Returns:

the variance

See Also:

Wikipedia: Variance

skew

@Deprecated
public double skew()

Deprecated. Not supported yet.

Description copied from interface: ProbabilityDistribution

Get the skewness of this distribution.

Specified by:

skew in interface ProbabilityDistribution

Returns:

the skewness

See Also:

Wikipedia: Skewness

kurtosis

@Deprecated
public double kurtosis()

Deprecated. Not supported yet.

Description copied from interface: ProbabilityDistribution

Get 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. Not supported yet.

Description copied from interface: ProbabilityDistribution

Get 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

Get 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)

the asymptotic distribution of the KolmogorovDistribution distribution

Parameters:

x -

Returns:

F(x)

See Also:

Wikipedia: KolmogorovDistribution distribution

quantile

@Deprecated
public double quantile(double u)

Deprecated. Not supported yet.

Description copied from interface: ProbabilityDistribution

Get 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. Not supported yet.

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:

• Wikipedia: Probability density function
• Wikipedia: Probability mass function

moment

@Deprecated
public double moment(double x)

Deprecated. Not supported yet.

Description copied from interface: ProbabilityDistribution

The moment generating function is the expected value of e^tX. That is,

E(e^tX)

This may not always exist.

Specified by:

moment in interface ProbabilityDistribution

Parameters:

x - x

Returns:

E(exp(tX))

See Also:

Wikipedia: Moment-generating function