Class KolmogorovTwoSamplesDistribution
- java.lang.Object
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- dev.nm.stat.test.distribution.kolmogorov.KolmogorovTwoSamplesDistribution
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- 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."
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Nested Class Summary
Nested Classes Modifier and Type Class Description static classKolmogorovTwoSamplesDistribution.Sidethe available types of Kolmogorov-Smirnov two-sample test
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Constructor Summary
Constructors Constructor 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.
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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)Deprecated.doubleentropy()Deprecated.doublekurtosis()Deprecated.doublemean()Deprecated.doublemedian()Deprecated.doublemoment(double x)Deprecated.doublequantile(double q)Deprecated.doubleskew()Deprecated.doublevariance()Deprecated.
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Constructor Detail
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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 1n2- the size of sample 2samples- the concatenation of the two samples in ascending orderside- one-sided or two-sided testbigN- the threshold to use the asymptotic distribution when n > bigN
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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 1n2- the size of sample 2side- one-sided or two-sided testbigN- the threshold to use the asymptotic distribution when n > bigN
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KolmogorovTwoSamplesDistribution
public KolmogorovTwoSamplesDistribution(int n1, int n2, KolmogorovTwoSamplesDistribution.Side side, double[] samples)Construct a two-sample Kolmogorov distribution.- Parameters:
n1- the size of sample 1n2- the size of sample 2side- one-sided or two-sided testsamples- the concatenation of the two samples in ascending order
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KolmogorovTwoSamplesDistribution
public KolmogorovTwoSamplesDistribution(double[] sample1, double[] sample2, KolmogorovTwoSamplesDistribution.Side side)Construct a two-sample Kolmogorov distribution.- Parameters:
sample1- sample 1sample2- sample 2side- one-sided or two-sided test
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Method Detail
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mean
@Deprecated public double mean()
Deprecated.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
@Deprecated public double variance()
Deprecated.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
@Deprecated public double quantile(double q)
Deprecated.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:
q-u, a quantile- Returns:
- F-1(u)
- See Also:
- Wikipedia: Quantile function
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density
@Deprecated public double density(double x)
Deprecated.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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