dev.nm.stat.test.distribution.kolmogorov

Class KolmogorovTwoSamplesDistribution

java.lang.Object

dev.nm.stat.test.distribution.kolmogorov.KolmogorovTwoSamplesDistribution

All Implemented Interfaces:

ProbabilityDistribution

public class KolmogorovTwoSamplesDistribution
extends Object
implements ProbabilityDistribution

Compute the p-values for the generalized (conditionally distribution-free) Smirnov homogeneity test. That is, \[ P(D_{m,n} \geq c | H_0) = 1 - P(D_{m,n} c | H_0) = 1 - \textup{cdf}(c) \] where \[ D_{m,n} = \max \left | S_m(x) - S_n(x) \right | \]

See Also:

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

Nested Class Summary

Nested Classes

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

Constructor Summary

Constructors

Constructor and Description
KolmogorovTwoSamplesDistribution(double[] sample1, double[] sample2, KolmogorovTwoSamplesDistribution.Side side) Construct a two-sample Kolmogorov distribution.
KolmogorovTwoSamplesDistribution(int n1, int n2, double[] samples, KolmogorovTwoSamplesDistribution.Side side, int bigN) Construct a two-sample Kolmogorov distribution.
KolmogorovTwoSamplesDistribution(int n1, int n2, KolmogorovTwoSamplesDistribution.Side side, double[] samples) Construct a two-sample Kolmogorov distribution.
KolmogorovTwoSamplesDistribution(int n1, int n2, KolmogorovTwoSamplesDistribution.Side side, int bigN) Construct a two-sample Kolmogorov distribution, assuming that there is no tie in the samples.

Method Summary

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

KolmogorovTwoSamplesDistribution

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

Construct a two-sample Kolmogorov distribution.

Parameters:

n1 - the size of sample 1

n2 - the size of sample 2

samples - the concatenation of the two samples in ascending order

side - one-sided or two-sided test

bigN - the threshold to use the asymptotic distribution when n > bigN

KolmogorovTwoSamplesDistribution

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

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

Parameters:

n1 - the size of sample 1

n2 - the size of sample 2

side - one-sided or two-sided test

bigN - the threshold to use the asymptotic distribution when n > bigN

KolmogorovTwoSamplesDistribution

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

Construct a two-sample Kolmogorov distribution.

Parameters:

n1 - the size of sample 1

n2 - the size of sample 2

side - one-sided or two-sided test

samples - the concatenation of the two samples in ascending order

KolmogorovTwoSamplesDistribution

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

Construct a two-sample Kolmogorov distribution.

Parameters:

sample1 - sample 1

sample2 - sample 2

side - one-sided or two-sided test

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 x)

Description copied from interface: ProbabilityDistribution

Gets 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.

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. \[ \begin{gathered} F^{-1}(u) = x, such that \\ Pr(X \le x) = u \end{gathered} \] 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.

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.

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 - t

Returns:

E(exp(tX))

See Also:

Wikipedia: Moment-generating function