Class KolmogorovOneSidedDistribution
- java.lang.Object
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- dev.nm.stat.test.distribution.kolmogorov.KolmogorovOneSidedDistribution
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- All Implemented Interfaces:
ProbabilityDistribution
public class KolmogorovOneSidedDistribution extends Object implements ProbabilityDistribution
Compute the probability that F(x) is dominated by the upper confidence contour, for all x:Pn(ε) = Pr{F(x) < min{Fn(x) + ε, 1}}
- See Also:
- "Z. W. Birnbaum and Fred H. Tingey, "One-sided confidence contours for probability distribution functions," The Annals of Mathematical Statistics, Vol. 22, No. 4 (Dec., 1951), p. 592-596."
- "N. Smirnov, "Sur les 6carts de la courbe de distribution empirique," Rec. Math. (Mat.Sbornik), N. S. Vol. 6 (48) (1939), p. 3-26."
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Constructor Summary
Constructors Constructor Description KolmogorovOneSidedDistribution(int n)Construct a one-sided Kolmogorov distribution.KolmogorovOneSidedDistribution(int n, int bigN)Construct a one-sided Kolmogorov distribution.
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Method Summary
All Methods Static Methods Instance Methods Concrete Methods Deprecated Methods Modifier and Type Method Description static doubleasymptoticCDF(double m, double x)This is the asymptotic distribution of the one-sided Kolmogorov distribution.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)Gets the quantile, the inverse of the cumulative distribution function.doubleskew()Deprecated.doublevariance()Deprecated.
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Constructor Detail
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KolmogorovOneSidedDistribution
public KolmogorovOneSidedDistribution(int n, int bigN)Construct a one-sided Kolmogorov distribution.- Parameters:
n- the number of observationsbigN- the threshold to use the asymptotic distribution when n > bigN
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KolmogorovOneSidedDistribution
public KolmogorovOneSidedDistribution(int n)
Construct a one-sided Kolmogorov distribution. We use the asymptotic distribution for n > 50.- Parameters:
n- the number of observations
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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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asymptoticCDF
public static double asymptoticCDF(double m, double x)This is the asymptotic distribution of the one-sided Kolmogorov distribution.- Parameters:
m- a scaling factor; usually a function of the size of the sample(s)x- x- Returns:
- Pr(x)
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quantile
public double quantile(double q)
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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