Package dev.nm.stat.test.rank.wilcoxon
Class WilcoxonRankSumDistribution
- java.lang.Object
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- dev.nm.stat.test.rank.wilcoxon.WilcoxonRankSumDistribution
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- All Implemented Interfaces:
ProbabilityDistribution
public class WilcoxonRankSumDistribution extends Object implements ProbabilityDistribution
Compute the exact distribution of the Wilcoxon rank sum test statistic. Let x and y be two random, independent samples of sizes 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 aredwilcox, pwilcox, qwilcox, rwilcox.
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Constructor Summary
Constructors Constructor Description WilcoxonRankSumDistribution(int M, int N)Construct a Wilcoxon Rank Sum distribution for sample sizesMandN.
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Method Summary
All Methods Instance Methods Concrete Methods Deprecated Methods Modifier and Type Method Description doublecdf(double x)Gets the cumulative probability F(x) = Pr(X ≤ x).doubledensity(double x)The density function, which, if exists, is the derivative of F.doubleentropy()Deprecated.doublekurtosis()Deprecated.doublemean()Gets the mean of this distribution.doublemedian()Deprecated.doublemoment(double x)Deprecated.doublepValue(double x)Compute the two-sided p-value for a critical value.doublequantile(double u)Gets the quantile, the inverse of the cumulative distribution function.doublerightOneSidedPvalue(double x)Compute the one-sided p-value for the statistic greater than a critical value.doubleskew()Deprecated.doublevariance()Gets the variance of this distribution.
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Method Detail
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mean
public double mean()
Description copied from interface:ProbabilityDistributionGets the mean of this distribution.- Specified by:
meanin interfaceProbabilityDistribution- Returns:
- the mean
- See Also:
- Wikipedia: Expected value
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median
@Deprecated public double median()
Deprecated.Description copied from interface:ProbabilityDistributionGets the median of this distribution.- Specified by:
medianin interfaceProbabilityDistribution- Returns:
- the median
- See Also:
- Wikipedia: Median
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variance
public double variance()
Description copied from interface:ProbabilityDistributionGets the variance of this distribution.- Specified by:
variancein interfaceProbabilityDistribution- Returns:
- the variance
- See Also:
- Wikipedia: Variance
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skew
@Deprecated public double skew()
Deprecated.Description copied from interface:ProbabilityDistributionGets the skewness of this distribution.- Specified by:
skewin interfaceProbabilityDistribution- Returns:
- the skewness
- See Also:
- Wikipedia: Skewness
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kurtosis
@Deprecated public double kurtosis()
Deprecated.Description copied from interface:ProbabilityDistributionGets the excess kurtosis of this distribution.- Specified by:
kurtosisin interfaceProbabilityDistribution- Returns:
- the excess kurtosis
- See Also:
- Wikipedia: Kurtosis
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entropy
@Deprecated public double entropy()
Deprecated.Description copied from interface:ProbabilityDistributionGets the entropy of this distribution.- Specified by:
entropyin interfaceProbabilityDistribution- Returns:
- the entropy
- See Also:
- Wikipedia: Entropy (information theory)
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cdf
public double cdf(double x)
Description copied from interface:ProbabilityDistributionGets the cumulative probability F(x) = Pr(X ≤ x).- Specified by:
cdfin interfaceProbabilityDistribution- Parameters:
x- x- Returns:
- F(x) = Pr(X ≤ x)
- See Also:
- Wikipedia: Cumulative distribution function
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quantile
public double quantile(double u)
Description copied from interface:ProbabilityDistributionGets 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.
This may not always exist.F-1(u) = x, such that Pr(X ≤ x) = u
- Specified by:
quantilein interfaceProbabilityDistribution- Parameters:
u-u, a quantile- Returns:
- F-1(u)
- See Also:
- Wikipedia: Quantile function
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density
public double density(double x)
Description copied from interface:ProbabilityDistributionThe 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:
densityin interfaceProbabilityDistribution- Parameters:
x- x- Returns:
- f(x)
- See Also:
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moment
@Deprecated public double moment(double x)
Deprecated.Description copied from interface:ProbabilityDistributionThe moment generating function is the expected value of etX. That is,E(etX)
This may not always exist.- Specified by:
momentin interfaceProbabilityDistribution- Parameters:
x- t- Returns:
- E(exp(tX))
- See Also:
- Wikipedia: Moment-generating function
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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 right, one-sided p-value
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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
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