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

Class KolmogorovTwoSamplesDistribution

java.lang.Object

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

All Implemented Interfaces:

ProbabilityDistribution, java.io.Serializable

public class KolmogorovTwoSamplesDistribution
extends java.lang.Object
implements ProbabilityDistribution

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."

, Serialized Form

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	KolmogorovTwoSamplesDistribution.Side the types of KolmogorovDistribution two-sample test available

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 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

Constructors

Constructor and Description
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

Modifier and Type	Method and Description
double	cdf(double x) 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 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: 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 x)

Description copied from interface: ProbabilityDistribution

Get the cumulative probability F(x) = Pr(X ≤ x).

Specified by:

cdf in interface ProbabilityDistribution

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: 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:

q - 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