Extends the class ContinuousDistribution for the Kolmogorov-Smirnov distribution with parameter \(n\) [55] . More...
Public Member Functions | |
| KolmogorovSmirnovDist (int n) | |
| Constructs a Kolmogorov–Smirnov distribution with parameter \(n\). More... | |
| double | density (double x) |
| double | cdf (double x) |
| Returns the distribution function \(F(x)\). More... | |
| double | barF (double x) |
| Returns \(\bar{F}(x) = 1 - F(x)\). More... | |
| double | inverseF (double u) |
| Returns the inverse distribution function \(F^{-1}(u)\), defined in ( inverseF ). More... | |
| int | getN () |
| Returns the parameter \(n\) of this object. | |
| void | setN (int n) |
| Sets the parameter \(n\) of this object. | |
| double [] | getParams () |
| Returns an array containing the parameter \(n\) of this object. | |
| String | toString () |
Returns a String containing information about the current distribution. | |
 Public Member Functions inherited from ContinuousDistribution | |
| abstract double | density (double x) |
| Returns \(f(x)\), the density evaluated at \(x\). More... | |
| double | barF (double x) |
| Returns the complementary distribution function. More... | |
| double | inverseBrent (double a, double b, double u, double tol) |
| Computes the inverse distribution function \(x = F^{-1}(u)\), using the Brent-Dekker method. More... | |
| double | inverseBisection (double u) |
| Computes and returns the inverse distribution function \(x = F^{-1}(u)\), using bisection. More... | |
| double | inverseF (double u) |
| Returns the inverse distribution function \(x = F^{-1}(u)\). More... | |
| double | getMean () |
| Returns the mean. More... | |
| double | getVariance () |
| Returns the variance. More... | |
| double | getStandardDeviation () |
| Returns the standard deviation. More... | |
| double | getXinf () |
| Returns \(x_a\) such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\). More... | |
| double | getXsup () |
| Returns \(x_b\) such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\). More... | |
| void | setXinf (double xa) |
Sets the value \(x_a=\) xa, such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\). More... | |
| void | setXsup (double xb) |
Sets the value \(x_b=\) xb, such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\). More... | |
Static Public Member Functions | |
| static double | density (int n, double x) |
| Computes the density for the Kolmogorov–Smirnov distribution with parameter \(n\). | |
| static double | cdf (int n, double x) |
| Computes the Kolmogorov–Smirnov distribution function \(F(x)\) with parameter \(n\) using Durbin’s matrix formula [55] . More... | |
| static double | barF (int n, double x) |
| Computes the complementary distribution function \(\bar{F}(x)\) with parameter \(n\). More... | |
| static double | inverseF (int n, double u) |
| Computes the inverse \(x = F^{-1}(u)\) of the Kolmogorov–Smirnov distribution \(F(x)\) with parameter \(n\). | |
Protected Attributes | |
| int | n |
| Protected Attributes inherited from ContinuousDistribution | |
| double | supportA = Double.NEGATIVE_INFINITY |
| double | supportB = Double.POSITIVE_INFINITY |
Static Protected Attributes | |
| static final int | NEXACT = 500 |
| Static Protected Attributes inherited from ContinuousDistribution | |
| static final double | XBIG = 100.0 |
| static final double | XBIGM = 1000.0 |
| static final double [] | EPSARRAY |
Additional Inherited Members | |
| Public Attributes inherited from ContinuousDistribution | |
| int | decPrec = 15 |
Detailed Description
Extends the class ContinuousDistribution for the Kolmogorov-Smirnov distribution with parameter \(n\) [55] .
Given an empirical distribution \(F_n\) with \(n\) independent observations and a continuous distribution \(F(x)\), the two-sided Kolmogorov–Smirnov statistic is defined as
\[ D_n = \sup_{-\infty\le x \le\infty} |F_n(x) - F(x)| = \max\{D_n^+, D_n^-\}, \]
where \(D_n^+\) and \(D_n^-\) are the Kolmogorov–Smirnov+ and Kolmogorov–Smirnov \(-\) statistics as defined in equations DNp and DNm of this guide. This class implements a high precision version of the Kolmogorov–Smirnov distribution \(P[D_n \le x]\); it is a Java translation of the \(C\) program written in [175] . According to its authors, it should give 13 decimal digits of precision. It is extremely slow for large values of \(n\).
Constructor & Destructor Documentation
◆ KolmogorovSmirnovDist()
| KolmogorovSmirnovDist | ( | int | n | ) |
Constructs a Kolmogorov–Smirnov distribution with parameter \(n\).
Restriction: \(n \ge1\).
Member Function Documentation
◆ barF() [1/2]
| double barF | ( | double | x | ) |
Returns \(\bar{F}(x) = 1 - F(x)\).
- Parameters
-
x value at which the complementary distribution function is evaluated
- Returns
- complementary distribution function evaluated at
x
Implements Distribution.
◆ barF() [2/2]
|
static |
Computes the complementary distribution function \(\bar{F}(x)\) with parameter \(n\).
Simply returns 1 - cdf(n,x). It is not precise in the upper tail.
◆ cdf() [1/2]
| double cdf | ( | double | x | ) |
Returns the distribution function \(F(x)\).
- Parameters
-
x value at which the distribution function is evaluated
- Returns
- distribution function evaluated at
x
Implements Distribution.
◆ cdf() [2/2]
|
static |
◆ inverseF()
| double inverseF | ( | double | u | ) |
Returns the inverse distribution function \(F^{-1}(u)\), defined in ( inverseF ).
- Parameters
-
u value in the interval \((0,1)\) for which the inverse distribution function is evaluated
- Returns
- the inverse distribution function evaluated at
u
Implements Distribution.
The documentation for this class was generated from the following file:
- KolmogorovSmirnovDist.java
