Apache Commons Math 3.6.1 · org.apache.commons.math3.distribution.KolmogorovSmirnovDistribution

Implementation of the Kolmogorov-Smirnov distribution.

Treats the distribution of the two-sided P(D_n < d) where D_n = sup_x |G(x) - G_n (x)| for the theoretical cdf G and the empirical cdf G_n.

This implementation is based on [1] with certain quick decisions for extreme values given in [2].

In short, when wanting to evaluate P(D_n < d), the method in [1] is to write d = (k - h) / n for positive integer k and 0 <= h < 1. Then P(D_n < d) = (n! / n^n) * t_kk, where t_kk is the (k, k)'th entry in the special matrix H^n, i.e. H to the n'th power.

References:

[1] Evaluating Kolmogorov's Distribution by George Marsaglia, Wai Wan Tsang, and Jingbo Wang
[2] Computing the Two-Sided Kolmogorov-Smirnov Distribution by Richard Simard and Pierre L'Ecuyer

Note that [1] contains an error in computing h, refer to MATH-437 for details.

Field Summary

Modifier and Type	Field and Description
private int	n Number of observations.
private static final long	serialVersionUID Serializable version identifier.

Constructor Summary

Access	Constructor and Description
public	KolmogorovSmirnovDistribution(int Number of observations n)

Method Summary

Modifier and Type	Method and Description
public double	Returns: the two-sided probability of `P(D_n < d)` cdf(double statistic d) Calculates `P(D_n < d)` using method described in [1] with quick decisions for extreme values given in [2] (see above).
public double	Returns: the two-sided probability of `P(D_n < d)` cdf(double statistic d, boolean whether the probability should be calculated exact using `org.apache.commons.math3.fraction.BigFraction` everywhere at the expense of very slow execution time, or if `double` should be used convenient places to gain speed. Almost never choose `true` in real applications unless you are very sure; `true` is almost solely for verification purposes. exact) Calculates `P(D_n < d)` using method described in [1] with quick decisions for extreme values given in [2] (see above).
public double	Returns: the two-sided probability of `P(D_n < d)` cdfExact(double statistic d) Calculates `P(D_n < d)` using method described in [1] with quick decisions for extreme values given in [2] (see above).
private FieldMatrix<BigFraction>	Returns: H matrix createH(double statistic d) Creates `H` of size `m x m` as described in [1] (see above).
private double	Returns: the two-sided probability of `P(D_n < d)` exactK(double statistic d) Calculates the exact value of `P(D_n < d)` using method described in [1] and `org.apache.commons.math3.fraction.BigFraction` (see above).
private double	Returns: the two-sided probability of `P(D_n < d)` roundedK(double statistic d) Calculates `P(D_n < d)` using method described in [1] and doubles (see above).

Inherited from java.lang.Object:: clone equals finalize getClass hashCode notify notifyAll toString wait wait wait

Field Detail

n	back to summary
private int n Number of observations.

serialVersionUID	back to summary
private static final long serialVersionUID Serializable version identifier.

Constructor Detail

KolmogorovSmirnovDistribution	back to summary
public KolmogorovSmirnovDistribution(int n) throws NotStrictlyPositiveException Parameters n:int Number of observations Exceptions NotStrictlyPositiveException: if `n <= 0`

Method Detail

cdf back to summary

cdf	back to summary
public double cdf(double d) throws MathArithmeticException Calculates `P(D_n < d)` using method described in [1] with quick decisions for extreme values given in [2] (see above). The result is not exact as with `KolmogorovSmirnovDistribution#cdfExact(double)` because calculations are based on `double` rather than `org.apache.commons.math3.fraction.BigFraction`. Parameters d:double statistic Returns:double the two-sided probability of `P(D_n < d)` Exceptions MathArithmeticException: if algorithm fails to convert `h` to a `org.apache.commons.math3.fraction.BigFraction` in expressing `d` as `(k - h) / m` for integer `k, m` and `0 <= h < 1`.

public double cdf(double d) throws MathArithmeticException

Calculates P(D_n < d) using method described in [1] with quick decisions for extreme values given in [2] (see above). The result is not exact as with KolmogorovSmirnovDistribution#cdfExact(double) because calculations are based on double rather than org.apache.commons.math3.fraction.BigFraction.

Parameters

d:double: statistic

Returns:double

the two-sided probability of P(D_n < d)

Exceptions

MathArithmeticException:: if algorithm fails to convert h to a org.apache.commons.math3.fraction.BigFraction in expressing d as (k - h) / m for integer k, m and 0 <= h < 1.

cdf back to summary

cdf	back to summary
public double cdf(double d, boolean exact) throws MathArithmeticException Calculates `P(D_n < d)` using method described in [1] with quick decisions for extreme values given in [2] (see above). Parameters d:double statistic exact:boolean whether the probability should be calculated exact using `org.apache.commons.math3.fraction.BigFraction` everywhere at the expense of very slow execution time, or if `double` should be used convenient places to gain speed. Almost never choose `true` in real applications unless you are very sure; `true` is almost solely for verification purposes. Returns:double the two-sided probability of `P(D_n < d)` Exceptions MathArithmeticException: if algorithm fails to convert `h` to a `org.apache.commons.math3.fraction.BigFraction` in expressing `d` as `(k - h) / m` for integer `k, m` and `0 <= h < 1`.

public double cdf(double d, boolean exact) throws MathArithmeticException

Calculates P(D_n < d) using method described in [1] with quick decisions for extreme values given in [2] (see above).

Parameters

d:double: statistic
exact:boolean: whether the probability should be calculated exact using org.apache.commons.math3.fraction.BigFraction everywhere at the expense of very slow execution time, or if double should be used convenient places to gain speed. Almost never choose true in real applications unless you are very sure; true is almost solely for verification purposes.

Returns:double

the two-sided probability of P(D_n < d)

Exceptions

MathArithmeticException:: if algorithm fails to convert h to a org.apache.commons.math3.fraction.BigFraction in expressing d as (k - h) / m for integer k, m and 0 <= h < 1.

cdfExact back to summary

cdfExact	back to summary
public double cdfExact(double d) throws MathArithmeticException Calculates `P(D_n < d)` using method described in [1] with quick decisions for extreme values given in [2] (see above). The result is exact in the sense that BigFraction/BigReal is used everywhere at the expense of very slow execution time. Almost never choose this in real applications unless you are very sure; this is almost solely for verification purposes. Normally, you would choose `KolmogorovSmirnovDistribution#cdf(double)` Parameters d:double statistic Returns:double the two-sided probability of `P(D_n < d)` Exceptions MathArithmeticException: if algorithm fails to convert `h` to a `org.apache.commons.math3.fraction.BigFraction` in expressing `d` as `(k - h) / m` for integer `k, m` and `0 <= h < 1`.

public double cdfExact(double d) throws MathArithmeticException

Calculates P(D_n < d) using method described in [1] with quick decisions for extreme values given in [2] (see above). The result is exact in the sense that BigFraction/BigReal is used everywhere at the expense of very slow execution time. Almost never choose this in real applications unless you are very sure; this is almost solely for verification purposes. Normally, you would choose KolmogorovSmirnovDistribution#cdf(double)

Parameters

d:double: statistic

Returns:double

the two-sided probability of P(D_n < d)

Exceptions

MathArithmeticException:: if algorithm fails to convert h to a org.apache.commons.math3.fraction.BigFraction in expressing d as (k - h) / m for integer k, m and 0 <= h < 1.

createH back to summary

createH	back to summary
private FieldMatrix<BigFraction> createH(double d) throws NumberIsTooLargeException, FractionConversionException Creates `H` of size `m x m` as described in [1] (see above). Parameters d:double statistic Returns:FieldMatrix<BigFraction> H matrix Exceptions NumberIsTooLargeException: if fractional part is greater than 1 FractionConversionException: if algorithm fails to convert `h` to a `org.apache.commons.math3.fraction.BigFraction` in expressing `d` as `(k - h) / m` for integer `k, m` and `0 <= h < 1`.

private FieldMatrix<BigFraction> createH(double d) throws NumberIsTooLargeException, FractionConversionException

Creates H of size m x m as described in [1] (see above).

Parameters

d:double: statistic

Returns:FieldMatrix<BigFraction>

H matrix

Exceptions

NumberIsTooLargeException:: if fractional part is greater than 1
FractionConversionException:: if algorithm fails to convert h to a org.apache.commons.math3.fraction.BigFraction in expressing d as (k - h) / m for integer k, m and 0 <= h < 1.

exactK back to summary

exactK	back to summary
private double exactK(double d) throws MathArithmeticException Calculates the exact value of `P(D_n < d)` using method described in [1] and `org.apache.commons.math3.fraction.BigFraction` (see above). Parameters d:double statistic Returns:double the two-sided probability of `P(D_n < d)` Exceptions MathArithmeticException: if algorithm fails to convert `h` to a `org.apache.commons.math3.fraction.BigFraction` in expressing `d` as `(k - h) / m` for integer `k, m` and `0 <= h < 1`.

private double exactK(double d) throws MathArithmeticException

Calculates the exact value of P(D_n < d) using method described in [1] and org.apache.commons.math3.fraction.BigFraction (see above).

Parameters

d:double: statistic

Returns:double

the two-sided probability of P(D_n < d)

Exceptions

MathArithmeticException:: if algorithm fails to convert h to a org.apache.commons.math3.fraction.BigFraction in expressing d as (k - h) / m for integer k, m and 0 <= h < 1.

roundedK back to summary

roundedK	back to summary
private double roundedK(double d) throws MathArithmeticException Calculates `P(D_n < d)` using method described in [1] and doubles (see above). Parameters d:double statistic Returns:double the two-sided probability of `P(D_n < d)` Exceptions MathArithmeticException: if algorithm fails to convert `h` to a `org.apache.commons.math3.fraction.BigFraction` in expressing `d` as `(k - h) / m` for integer `k, m` and `0 <= h < 1`.

private double roundedK(double d) throws MathArithmeticException

Calculates P(D_n < d) using method described in [1] and doubles (see above).

Parameters

d:double: statistic

Returns:double

the two-sided probability of P(D_n < d)

Exceptions

MathArithmeticException:: if algorithm fails to convert h to a org.apache.commons.math3.fraction.BigFraction in expressing d as (k - h) / m for integer k, m and 0 <= h < 1.

public Class KolmogorovSmirnovDistribution

Field Summary

Constructor Summary

Method Summary

Field Detail

Constructor Detail

Method Detail