WilcoxonRankSumDistribution (SuanShuExtension API)

java.lang.Object
- com.numericalmethod.suanshu.stats.test.rank.wilcoxon.WilcoxonRankSumDistribution

All Implemented Interfaces:

ProbabilityDistribution, java.io.Serializable
```
public class WilcoxonRankSumDistribution
extends java.lang.Object
implements ProbabilityDistribution
```
Compute the exact distribution of the Wilcoxon rank sum test statistic.
Let x and y be two random, independent samples of size M and N. The Wilcoxon rank sum statistic is the number of all pairs (x[i], y[j]) for which y[j] is not greater than x[i]. This statistic takes values between 0 and M * N.
The R equivalent functions are dwilcox, pwilcox, qwilcox, rwilcox.

See Also:

"Zbynek Sidak, Pranab K. Sen, Jaroslav Hajek. Theory of Rank Tests. Theorems 1, Section 5.3, p.173.", Serialized Form

Field Summary

Fields
Modifier and Type Field and Description

int M
number of observations in group 1

int N
number of observations in group 2

Fields
Modifier and Type	Field and Description
`int`	`M` number of observations in group 1
`int`	`N` number of observations in group 2

Constructor Summary

Constructors
Constructor and Description

WilcoxonRankSumDistribution(int M, int N)
Construct a Wilcoxon Rank Sum distribution for sample sizes M and N.

Constructors
Constructor and Description
`WilcoxonRankSumDistribution(int M, int N)` Construct a Wilcoxon Rank Sum distribution for sample sizes `M` and `N`.

Method Summary

All Methods Instance Methods Concrete Methods Deprecated Methods
Modifier and Type	Method and Description
`double`	`cdf(double x)` Get 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. Not supported yet.
`double`	`kurtosis()` Deprecated. Not supported yet.
`double`	`mean()` Get the mean of this distribution.
`double`	`median()` Deprecated. Not supported yet.
`double`	`moment(double x)` Deprecated. Not supported yet.
`double`	`pValue(double x)` Compute the two-sided p-value for a critical value.
`double`	`pValue1SidedGreater(double x)` Compute the one-sided p-value for the statistics greater than a critical value.
`double`	`quantile(double u)` Get the quantile, the inverse of the cumulative distribution function.
`double`	`skew()` Deprecated. Not supported yet.
`double`	`variance()` Get the variance of this distribution.

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- Field Detail
  - M
```
public final int M
```
    number of observations in group 1
  - N
```
public final int N
```
    number of observations in group 2
- Constructor Detail
  - WilcoxonRankSumDistribution
```
public WilcoxonRankSumDistribution(int M,
                                   int N)
```
    Construct a Wilcoxon Rank Sum distribution for sample sizes M and N.
    
    Parameters:
    
    M - number of observations in group 1
    
    N - number of observations in group 2
- Method Detail
  - mean
```
public double mean()
```
    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
```
public double variance()
```
    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
```
public double quantile(double u)
```
    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
```
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. 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
  - pValue1SidedGreater
```
public double pValue1SidedGreater(double x)
```
    Compute the one-sided p-value for the statistics 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 two-sided p-value

Class WilcoxonRankSumDistribution

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

M

N

Constructor Detail

WilcoxonRankSumDistribution

Method Detail

mean

median

variance

skew

kurtosis

entropy

cdf

quantile

density

moment

pValue1SidedGreater

pValue