Package dev.nm.stat.test.rank.wilcoxon

Class WilcoxonSignedRankDistribution

java.lang.Object

dev.nm.stat.test.rank.wilcoxon.WilcoxonSignedRankDistribution

All Implemented Interfaces:

ProbabilityDistribution

public class WilcoxonSignedRankDistribution
extends Object
implements ProbabilityDistribution

Compute the exact distribution of the Wilcoxon signed rank test statistic.

Let x be a sample of size N from a continuous distribution symmetric about the origin. The Wilcoxon signed rank statistic is the sum of the ranks of the absolute values x[i] for which x[i] are positive. This statistic takes values between 0 and N(N+1)/2.

The R equivalent functions are dsignrank, pdsignrank, qdsignrank, rdsignrank.

Constructor Summary

Constructors

Constructor	Description
WilcoxonSignedRankDistribution(int N)	Construct a Wilcoxon Signed Rank distribution for a sample size N.

Method Summary

Modifier and Type	Method	Description
double	cdf(double x)	Gets the cumulative probability F(x) = Pr(X ≤ x).
double	density(double x)	The density function, which, if exists, is the derivative of F.
double	entropy()	Deprecated.
double	kurtosis()	Deprecated.
double	mean()	Gets the mean of this distribution.
double	median()	Deprecated.
double	moment(double x)	Deprecated.
double	pValue(double x)	Compute the two-sided p-value for a critical value.
double	quantile(double u)	Gets the quantile, the inverse of the cumulative distribution function.
double	rightOneSidedPvalue(double x)	Compute the one-sided p-value for the statistic greater than a critical value.
double	skew()	Deprecated.
double	variance()	Gets the variance of this distribution.

Methods inherited from class java.lang.Object

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

Constructor Detail

WilcoxonSignedRankDistribution

public WilcoxonSignedRankDistribution(int N)

Construct a Wilcoxon Signed Rank distribution for a sample size N.

Parameters:

N - the number of observations

Method Detail

mean

public double mean()

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

public double variance()

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

public double quantile(double u)

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

public double density(double x)

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

rightOneSidedPvalue

public double rightOneSidedPvalue(double x)

Compute the one-sided p-value for the statistic greater than a critical value.

Parameters:

x - a critical value

Returns:

the one-sided p-value

pValue

public double pValue(double x)

Compute the two-sided p-value for a critical value.

Parameters:

x - a critical value

Returns:

the p-value