# SuanShu, a Java numerical and statistical library

com.numericalmethod.suanshu.stats.test.distribution.kolmogorov

## Class KolmogorovOneSidedDistribution

• java.lang.Object
• com.numericalmethod.suanshu.stats.test.distribution.kolmogorov.KolmogorovOneSidedDistribution
• 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}}
• "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."
• ### Constructor Summary

Constructors
Constructor and Description
KolmogorovOneSidedDistribution(int n)
Construct a one-sided Kolmogorov distribution.
KolmogorovOneSidedDistribution(int n, int bigN)
Construct a one-sided Kolmogorov distribution.
• ### Method Summary

All Methods
Modifier and Type Method and 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.
• ### Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
• ### Constructor Detail

• #### KolmogorovOneSidedDistribution

public KolmogorovOneSidedDistribution(int n,
int bigN)
Construct a one-sided Kolmogorov distribution.
Parameters:
n - the number of observations
bigN - the threshold to use the asymptotic distribution when n > bigN
• #### 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
• ### Method Detail

• #### mean

@Deprecated
public double mean()
Deprecated.
Description copied from interface: ProbabilityDistribution
Gets the mean of this distribution.
Specified by:
mean in interface ProbabilityDistribution
Returns:
the mean
Wikipedia: Expected value
• #### median

@Deprecated
public double median()
Deprecated.
Description copied from interface: ProbabilityDistribution
Gets the median of this distribution.
Specified by:
median in interface ProbabilityDistribution
Returns:
the median
Wikipedia: Median
• #### variance

@Deprecated
public double variance()
Deprecated.
Description copied from interface: ProbabilityDistribution
Gets the variance of this distribution.
Specified by:
variance in interface ProbabilityDistribution
Returns:
the variance
Wikipedia: Variance
• #### skew

@Deprecated
public double skew()
Deprecated.
Description copied from interface: ProbabilityDistribution
Gets the skewness of this distribution.
Specified by:
skew in interface ProbabilityDistribution
Returns:
the skewness
Wikipedia: Skewness
• #### kurtosis

@Deprecated
public double kurtosis()
Deprecated.
Description copied from interface: ProbabilityDistribution
Gets the excess kurtosis of this distribution.
Specified by:
kurtosis in interface ProbabilityDistribution
Returns:
the excess kurtosis
Wikipedia: Kurtosis
• #### entropy

@Deprecated
public double entropy()
Deprecated.
Description copied from interface: ProbabilityDistribution
Gets the entropy of this distribution.
Specified by:
entropy in interface ProbabilityDistribution
Returns:
the entropy
Wikipedia: Entropy (information theory)
• #### cdf

public double cdf(double x)
Description copied from interface: ProbabilityDistribution
Gets the cumulative probability F(x) = Pr(X ≤ x).
Specified by:
cdf in interface ProbabilityDistribution
Parameters:
x - x
Returns:
F(x) = Pr(X ≤ x)
Wikipedia: Cumulative distribution function
• #### 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)
"N. Smirnov, "Sur les 6carts de la courbe de distribution empirique," Rec. Math. (Mat.Sbornik), N. S. Vol. 6 (48) (1939), p. 3-26."
• #### 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.

F-1(u) = x, such that
Pr(X ≤ x) = u

This may not always exist.
Specified by:
quantile in interface ProbabilityDistribution
Parameters:
q - u, a quantile
Returns:
F-1(u)
Wikipedia: Quantile function
• #### 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 interface ProbabilityDistribution
Parameters:
x - x
Returns:
f(x)
• #### 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 interface ProbabilityDistribution
Parameters:
x - t
Returns:
E(exp(tX))