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

java.lang.Object
  com.numericalmethod.suanshu.stats.test.distribution.kolmogorov.KolmogorovTwoSamplesDistribution

All Implemented Interfaces:

UnivariateDistribution

public class KolmogorovTwoSamplesDistribution
extends java.lang.Object
implements UnivariateDistribution

Compute the p-values for the generalized (conditionally distribution-free) Smirnov homogeneity test.

That is, P(Dm,n ≥ c | H0) = 1 - P(Dm,n < c | H0) = 1 - cdf(c) , where Dm,n max |Sm(x) - Sn(x)|

See Also:

• "Algorithm AS 288: Exact Smirnov Two-Sample Tests for Arbitrary Distributions. Andrei M. Nikiforov, 1994. Royal Statistical Society."
• "Section 6.3. Nonparametric Statistical Inference. 4th edition. Jean Dickinson Gibbons, Subhabrata Chakraborti. CRC."

Nested Class Summary

static class

KolmogorovTwoSamplesDistribution.Side the types of KolmogorovDistribution two-sample test available

Field Summary

int	bigN the big N for which n > bigN we use the asymptotic distribution
int	n the total number of observations of the two samples
int	n1 the number of observations of the first sample
int	n2 the number of observations of the second sample
KolmogorovTwoSamplesDistribution.Side	side the type of KolmogorovDistribution two-sample distribution, i.e., equal, greater, less

Constructor Summary

KolmogorovTwoSamplesDistribution(double[] sample1, double[] sample2, KolmogorovTwoSamplesDistribution.Side side)
Construct a two-sample KolmogorovDistribution distribution.

KolmogorovTwoSamplesDistribution(int n1, int n2, double[] samples, KolmogorovTwoSamplesDistribution.Side side, int bigN)
Construct a two-sample KolmogorovDistribution distribution.

KolmogorovTwoSamplesDistribution(int n1, int n2, KolmogorovTwoSamplesDistribution.Side side, double[] samples)
Construct a two-sample KolmogorovDistribution distribution.

KolmogorovTwoSamplesDistribution(int n1, int n2, KolmogorovTwoSamplesDistribution.Side side, int bigN)
Construct a two-sample KolmogorovDistribution distribution, assuming that there is no tie in the samples.

Method Summary

double	cdf(double x) The cumulative distribution function.
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 q) 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

side

public final KolmogorovTwoSamplesDistribution.Side side

the type of KolmogorovDistribution two-sample distribution, i.e., equal, greater, less

bigN

public final int bigN

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

n1

public final int n1

the number of observations of the first sample

n2

public final int n2

the number of observations of the second sample

n

public final int n

the total number of observations of the two samples

Constructor Detail

KolmogorovTwoSamplesDistribution

public KolmogorovTwoSamplesDistribution(int n1,
                                        int n2,
                                        double[] samples,
                                        KolmogorovTwoSamplesDistribution.Side side,
                                        int bigN)

Construct a two-sample KolmogorovDistribution distribution.

Parameters:

n1 - size of sample 1

n2 - size of sample 2

samples - the concatenate of the two samples in ascending order

bigN - when n > bigN, we use the asymptotic distribution

KolmogorovTwoSamplesDistribution

public KolmogorovTwoSamplesDistribution(int n1,
                                        int n2,
                                        KolmogorovTwoSamplesDistribution.Side side,
                                        int bigN)

Construct a two-sample KolmogorovDistribution distribution, assuming that there is no tie in the samples.

Parameters:

n1 - size of sample 1

n2 - size of sample 2

bigN - when n > bigN, we use the asymptotic distribution

KolmogorovTwoSamplesDistribution

public KolmogorovTwoSamplesDistribution(int n1,
                                        int n2,
                                        KolmogorovTwoSamplesDistribution.Side side,
                                        double[] samples)

Construct a two-sample KolmogorovDistribution distribution.

Parameters:

n1 - size of sample 1

n2 - size of sample 2

side - the type of KolmogorovDistribution two-sample test

samples - the concatenate of the two samples in ascending order

KolmogorovTwoSamplesDistribution

public KolmogorovTwoSamplesDistribution(double[] sample1,
                                        double[] sample2,
                                        KolmogorovTwoSamplesDistribution.Side side)

Construct a two-sample KolmogorovDistribution distribution.

Parameters:

sample1 - sample 1

sample2 - sample 2

side - the type of KolmogorovDistribution two-sample test

Method Detail

mean

@Deprecated
public double mean()

Deprecated. Not supported yet.

Description copied from interface: UnivariateDistribution

Get the mean of this distribution.

Specified by:

mean in interface UnivariateDistribution

Returns:

the mean

See Also:

Wikipedia: Expected value

median

@Deprecated
public double median()

Deprecated. Not supported yet.

Description copied from interface: UnivariateDistribution

Get the median of this distribution.

Specified by:

median in interface UnivariateDistribution

Returns:

the median

See Also:

Wikipedia: Median

variance

@Deprecated
public double variance()

Deprecated. Not supported yet.

Description copied from interface: UnivariateDistribution

Get the variance of this distribution.

Specified by:

variance in interface UnivariateDistribution

Returns:

the variance

See Also:

Wikipedia: Variance

skew

@Deprecated
public double skew()

Deprecated. Not supported yet.

Description copied from interface: UnivariateDistribution

Get the skewness of this distribution.

Specified by:

skew in interface UnivariateDistribution

Returns:

the skewness

See Also:

Wikipedia: Skewness

kurtosis

@Deprecated
public double kurtosis()

Deprecated. Not supported yet.

Description copied from interface: UnivariateDistribution

Get the excess kurtosis of this distribution.

Specified by:

kurtosis in interface UnivariateDistribution

Returns:

the excess kurtosis

See Also:

Wikipedia: Kurtosis

entropy

@Deprecated
public double entropy()

Deprecated. Not supported yet.

Description copied from interface: UnivariateDistribution

Get the entropy of this distribution.

Specified by:

entropy in interface UnivariateDistribution

Returns:

the entropy

See Also:

Wikipedia: Entropy (information theory)

cdf

public double cdf(double x)

Description copied from interface: UnivariateDistribution

The cumulative distribution function.

F(x) = Pr(X <= x)

Specified by:

cdf in interface UnivariateDistribution

Parameters:

x - x

Returns:

F(x) = Pr(X <= x)

See Also:

Wikipedia: Cumulative distribution function

quantile

@Deprecated
public double quantile(double q)

Deprecated. Not supported yet.

Description copied from interface: UnivariateDistribution

The inverse of the cumulative distribution function. It returns the value below which random draws from the given 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 UnivariateDistribution

Parameters:

q - u

Returns:

F-1(u)

See Also:

Wikipedia: Quantile function

density

@Deprecated
public double density(double x)

Deprecated. Not supported yet.

Description copied from interface: UnivariateDistribution

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 UnivariateDistribution

Parameters:

x - x

Returns:

F(x) = Pr(X <= 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: UnivariateDistribution

The moment generating function, which is the expected value of

etX

This may not always exist.

Specified by:

moment in interface UnivariateDistribution

Parameters:

x - x

Returns:

E(exp(tX))

See Also:

Wikipedia: Moment-generating function