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 double
asymptoticCDF(double m, double x)
This is the asymptotic distribution of the one-sided Kolmogorov distribution.double
cdf(double x)
Gets the cumulative probability F(x) = Pr(X ≤ x).double
density(double x)
Deprecated.double
entropy()
Deprecated.double
kurtosis()
Deprecated.double
mean()
Deprecated.double
median()
Deprecated.double
moment(double x)
Deprecated.double
quantile(double q)
Gets the quantile, the inverse of the cumulative distribution function.double
skew()
Deprecated.double
variance()
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:ProbabilityDistribution
Gets the mean of this distribution.- Specified by:
mean
in interfaceProbabilityDistribution
- Returns:
- the mean
- See Also:
- Wikipedia: Expected value
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median
@Deprecated public double median()
Deprecated.Description copied from interface:ProbabilityDistribution
Gets the median of this distribution.- Specified by:
median
in interfaceProbabilityDistribution
- Returns:
- the median
- See Also:
- Wikipedia: Median
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variance
@Deprecated public double variance()
Deprecated.Description copied from interface:ProbabilityDistribution
Gets the variance of this distribution.- Specified by:
variance
in interfaceProbabilityDistribution
- Returns:
- the variance
- See Also:
- Wikipedia: Variance
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skew
@Deprecated public double skew()
Deprecated.Description copied from interface:ProbabilityDistribution
Gets the skewness of this distribution.- Specified by:
skew
in interfaceProbabilityDistribution
- Returns:
- the skewness
- See Also:
- Wikipedia: Skewness
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kurtosis
@Deprecated public double kurtosis()
Deprecated.Description copied from interface:ProbabilityDistribution
Gets the excess kurtosis of this distribution.- Specified by:
kurtosis
in interfaceProbabilityDistribution
- Returns:
- the excess kurtosis
- See Also:
- Wikipedia: Kurtosis
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entropy
@Deprecated public double entropy()
Deprecated.Description copied from interface:ProbabilityDistribution
Gets the entropy of this distribution.- Specified by:
entropy
in interfaceProbabilityDistribution
- Returns:
- the entropy
- See Also:
- Wikipedia: Entropy (information theory)
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cdf
public double cdf(double x)
Description copied from interface:ProbabilityDistribution
Gets the cumulative probability F(x) = Pr(X ≤ x).- Specified by:
cdf
in 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: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.
This may not always exist.F-1(u) = x, such that Pr(X ≤ x) = u
- Specified by:
quantile
in 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: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 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:ProbabilityDistribution
The moment generating function is the expected value of etX. That is,E(etX)
This may not always exist.- Specified by:
moment
in interfaceProbabilityDistribution
- Parameters:
x
- t- Returns:
- E(exp(tX))
- See Also:
- Wikipedia: Moment-generating function
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