Extends the class KolmogorovSmirnovDist for the Kolmogorov–Smirnov distribution. More...
Public Member Functions | |
| KolmogorovSmirnovDistQuick (int n) | |
| Constructs a Kolmogorov–Smirnov distribution with parameter \(n\). | |
| 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... | |
 Public Member Functions inherited from KolmogorovSmirnovDist | |
| 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 \(u = P[D_n \le x]\) with parameter \(n\), using the program described in [216] . More... | |
| static double | barF (int n, double x) |
| Computes the complementary Kolmogorov–Smirnov distribution \(P[D_n \ge x]\) with parameter \(n\), in a form that is more precise in the upper tail, using the program described in [216] . More... | |
| static double | inverseF (int n, double u) |
| Computes the inverse \(x = F^{-1}(u)\) of the distribution \(F(x)\) with parameter \(n\). | |
| Static Public Member Functions inherited from KolmogorovSmirnovDist | |
| 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 \(n\). | |
Additional Inherited Members | |
| Public Attributes inherited from ContinuousDistribution | |
| int | decPrec = 15 |
| Static Protected Member Functions inherited from KolmogorovSmirnovDist | |
| static double | densConnue (int n, double x) |
| static double | DurbinMatrix (int n, double d) |
| static double | cdfConnu (int n, double x) |
| static double | barFConnu (int n, double x) |
| static double | inverseConnue (int n, double u) |
| Protected Attributes inherited from KolmogorovSmirnovDist | |
| int | n |
| Protected Attributes inherited from ContinuousDistribution | |
| double | supportA = Double.NEGATIVE_INFINITY |
| double | supportB = Double.POSITIVE_INFINITY |
| Static Protected Attributes inherited from KolmogorovSmirnovDist | |
| 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 |
Detailed Description
Extends the class KolmogorovSmirnovDist for the Kolmogorov–Smirnov distribution.
The methods of this class are much faster than those of class KolmogorovSmirnovDist.
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 Kolmogorov–Smirnov distribution \(P[D_n \ge x]\) with parameter \(n\), in a form that is more precise in the upper tail, using the program described in [216] .
It returns at least 10 decimal digits of precision everywhere for all \(n \le500\), at least 6 decimal digits of precision for \(500 < n \le200000\), and a few correct decimal digits (1 to 5) for \(n > 200000\). This method is much faster and more precise for \(x\) close to 1, than method barF of KolmogorovSmirnovDist for moderate or large \(n\). Restriction: \(n\ge1\).
◆ 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 |
Computes the Kolmogorov–Smirnov distribution function \(u = P[D_n \le x]\) with parameter \(n\), using the program described in [216] .
This method uses Pomeranz’s recursion algorithm and the Durbin matrix algorithm [28], [205], [175] for \(n \le500\), which returns at least 13 decimal digits of precision. It uses the Pelz-Good asymptotic expansion [202] in the central part of the range for \(n > 500\) and returns at least 7 decimal digits of precision everywhere for \(500 < n \le100000\). For \(n > 100000\), it returns at least 5 decimal digits of precision for all \(u > 10^{-16}\), and a few correct decimals when \(u \le10^{-16}\). This method is much faster than method cdf of KolmogorovSmirnovDist for moderate or large \(n\). Restriction: \(n\ge1\).
◆ 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:
- KolmogorovSmirnovDistQuick.java
