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

java.lang.Object
  com.numericalmethod.suanshu.stats.test.distribution.kolmogorov.KolmogorovOneSidedDistribution

All Implemented Interfaces:

UnivariateDistribution

public class KolmogorovOneSidedDistribution
extends java.lang.Object
implements UnivariateDistribution

Compute Pn(ε) = Pr{F(x) < min{Fn(x) + ε, 1}, for all x}, i.e., the probability that F(x) is dominated by the upper confidence contour.

See Also:

• "One-sided confidence contours for probability distribution functions. Z. W. Birnbaum and Fred H. Tingey (1951). The Annals of Mathematical Statistics,Vol. 22, No. 4 (Dec., 1951), p. 592-596."
• "Sur les 6carts de la courbe de distribution empirique. N. Smirnov. Rec. Math. (Mat.Sbornik), N. S. Vol. 6 (48) (1939), p. 3-26."

Field Summary

int	bigN the big N for which n > bigN we use the asymptotic distribution
int	n the number of observations

Constructor Summary

KolmogorovOneSidedDistribution(int n)
Construct a one-sided Kolmogorov distribution.

KolmogorovOneSidedDistribution(int n, int bigN)
Construct a one-sided Kolmogorov distribution.

Method Summary

static double	asymptoticCDF(double m, double x) the asymptotic distribution of the one-sided Kolmogorov distribution
double	cdf(double x) The cumulative distribution function.
double	density(double x) Deprecated. Not supported yet.
double	entropy() Deprecated. Not supported yet.
double	kurtosis() Deprecated. Not supported yet.
double	mean() Deprecated. Not supported yet.
double	median() Deprecated. Not supported yet.
double	moment(double x) Deprecated. Not supported yet.
double	quantile(double q) The inverse of the cumulative distribution function.
double	skew() Deprecated. Not supported yet.
double	variance() Deprecated. Not supported yet.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

n

public final int n

the number of observations

bigN

public final int bigN

the big N for which n > bigN we use the asymptotic distribution

Constructor Detail

KolmogorovOneSidedDistribution

public KolmogorovOneSidedDistribution(int n,
                                      int bigN)

Construct a one-sided Kolmogorov distribution.

Parameters:

n - the number of observation

bigN - the big N for which n > bigN, we use the asymptotic distribution

KolmogorovOneSidedDistribution

public KolmogorovOneSidedDistribution(int n)

Construct a one-sided Kolmogorov distribution. We use the asymptotic distribution for n > 50.

Parameters:

n - the number of observation

Method Detail

mean

@Deprecated
public double mean()

Deprecated. Not supported yet.

Description copied from interface: UnivariateDistribution

Get the mean of this distribution.

Specified by:

mean in interface UnivariateDistribution

Returns:

the mean

See Also:

Wikipedia: Expected value

median

@Deprecated
public double median()

Deprecated. Not supported yet.

Description copied from interface: UnivariateDistribution

Get the median of this distribution.

Specified by:

median in interface UnivariateDistribution

Returns:

the median

See Also:

Wikipedia: Median

variance

@Deprecated
public double variance()

Deprecated. Not supported yet.

Description copied from interface: UnivariateDistribution

Get the variance of this distribution.

Specified by:

variance in interface UnivariateDistribution

Returns:

the variance

See Also:

Wikipedia: Variance

skew

@Deprecated
public double skew()

Deprecated. Not supported yet.

Description copied from interface: UnivariateDistribution

Get the skewness of this distribution.

Specified by:

skew in interface UnivariateDistribution

Returns:

the skewness

See Also:

Wikipedia: Skewness

kurtosis

@Deprecated
public double kurtosis()

Deprecated. Not supported yet.

Description copied from interface: UnivariateDistribution

Get the excess kurtosis of this distribution.

Specified by:

kurtosis in interface UnivariateDistribution

Returns:

the excess kurtosis

See Also:

Wikipedia: Kurtosis

entropy

@Deprecated
public double entropy()

Deprecated. Not supported yet.

Description copied from interface: UnivariateDistribution

Get the entropy of this distribution.

Specified by:

entropy in interface UnivariateDistribution

Returns:

the entropy

See Also:

Wikipedia: Entropy (information theory)

cdf

public double cdf(double x)

Description copied from interface: UnivariateDistribution

The cumulative distribution function.

F(x) = Pr(X <= x)

Specified by:

cdf in interface UnivariateDistribution

Parameters:

x - x

Returns:

F(x) = Pr(X <= x)

See Also:

Wikipedia: Cumulative distribution function

asymptoticCDF

public static double asymptoticCDF(double m,
                                   double x)

the asymptotic distribution of the one-sided Kolmogorov distribution

Parameters:

m - scaling factor; usually a function of the size of the sample(s)

x - x

Returns:

Pr(x)

See Also:

"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: UnivariateDistribution

The inverse of the cumulative distribution function. It returns the value below which random draws from the given 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 UnivariateDistribution

Parameters:

q - u

Returns:

F-1(u)

See Also:

Wikipedia: Quantile function

density

@Deprecated
public double density(double x)

Deprecated. Not supported yet.

Description copied from interface: UnivariateDistribution

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 UnivariateDistribution

Parameters:

x - x

Returns:

F(x) = Pr(X <= x)

See Also:

• Wikipedia: Probability density function
• Wikipedia: Probability mass function

moment

@Deprecated
public double moment(double x)

Deprecated. Not supported yet.

Description copied from interface: UnivariateDistribution

The moment generating function, which is the expected value of

etX

This may not always exist.

Specified by:

moment in interface UnivariateDistribution

Parameters:

x - x

Returns:

E(exp(tX))

See Also:

Wikipedia: Moment-generating function