dev.nm.stat.test.distribution.kolmogorov

Class KolmogorovOneSidedDistribution

java.lang.Object

dev.nm.stat.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: \[ Pn(\epsilon ) = Pr\{F(x) \lt \min\{Fn(x) + \epsilon , 1\}\} \]

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."

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

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

See Also:

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

See Also:

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

See Also:

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

See Also:

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

See Also:

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

See Also:

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)

See Also:

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)

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: 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. \[ \begin{gathered} F^{-1}(u) = x, such that \\ Pr(X \le x) = u \end{gathered} \] This may not always exist.

Specified by:

quantile in interface ProbabilityDistribution

Parameters:

q - u, a quantile

Returns:

\(F^{-1}(u)\)

See Also:

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)

See Also:

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

moment

@Deprecated
public double moment(double x)

Deprecated.

Description copied from interface: ProbabilityDistribution

The moment generating function is the expected value of \(e^{tX}\). That is, \[ E(e^{tX}) \] This may not always exist.

Specified by:

moment in interface ProbabilityDistribution

Parameters:

x - t

Returns:

E(exp(tX))

See Also:

Wikipedia: Moment-generating function