KolmogorovSmirnovPlusDist (Java Libraries for Stochastic Simulation)

java.lang.Object
- umontreal.iro.lecuyer.probdist.ContinuousDistribution
- - umontreal.iro.lecuyer.probdist.KolmogorovSmirnovPlusDist

All Implemented Interfaces:

Distribution
```
public class KolmogorovSmirnovPlusDist
extends ContinuousDistribution
```
Extends the class ContinuousDistribution for the Kolmogorov-Smirnov+ distribution (see). Given a sample of n independent uniforms U_i over [0, 1], the Kolmogorov-Smirnov+ statistic D_n⁺ and the Kolmogorov-Smirnov- statistic D_n^-, are defined by

D_n⁺ = max_{1 <= j <= n}(j/n - U_(j)),

D_n^- = max_{1 <= j <= n}(U_(j) - (j - 1)/n),

where the U_(j) are the U_i sorted in increasing order. Both statistics follows the same distribution function, i.e. F_n(x) = P[D_n⁺ <= x] = P[D_n^- <= x].

Field Summary
- Fields inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution
  decPrec

Constructor Summary

Constructors
Constructor and Description

KolmogorovSmirnovPlusDist(int n)
Constructs an Kolmogorov-Smirnov+ distribution for a sample of size n.

Constructors
Constructor and Description
`KolmogorovSmirnovPlusDist(int n)` Constructs an Kolmogorov-Smirnov+ distribution for a sample of size n.

Method Summary

Methods
Modifier and Type	Method and Description
`double`	`barF(double x)` Returns the complementary distribution function.
`static double`	`barF(int n, double x)` Computes the complementary distribution function bar(F)_n(x) with parameter n.
`double`	`cdf(double x)` Returns the distribution function F(x).
`static double`	`cdf(int n, double x)` Computes the Kolmogorov-Smirnov+ distribution function F_n(x) with parameter n.
`double`	`density(double x)` Returns f (x), the density evaluated at x.
`static double`	`density(int n, double x)` Computes the density of the Kolmogorov-Smirnov+ distribution with parameter n.
`int`	`getN()` Returns the parameter n of this object.
`double[]`	`getParams()` Returns an array containing the parameter n of this object.
`double`	`inverseF(double u)` Returns the inverse distribution function x = F^-1(u).
`static double`	`inverseF(int n, double u)` Computes the inverse x = F^-1(u) of the distribution with parameter n.
`void`	`setN(int n)` Sets the parameter n of this object.
`java.lang.String`	`toString()`

Methods inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution
getMean, getStandardDeviation, getVariance, getXinf, getXsup, inverseBisection, inverseBrent, setXinf, setXsup

Methods inherited from class java.lang.Object
equals, getClass, hashCode, notify, notifyAll, wait, wait, wait

- Constructor Detail
  - KolmogorovSmirnovPlusDist
```
public KolmogorovSmirnovPlusDist(int n)
```
    Constructs an Kolmogorov-Smirnov+ distribution for a sample of size n.
- Method Detail
  - density
```
public double density(double x)
```
    Description copied from class: ContinuousDistribution
    
    Returns f (x), the density evaluated at x.
    
    Specified by:
    
    density in class ContinuousDistribution
    
    Parameters:
    x - value at which the density is evaluated
    
    Returns:
    density function evaluated at x
  - cdf
```
public double cdf(double x)
```
    Description copied from interface: Distribution
    
    Returns the distribution function F(x).
    
    Parameters:
    x - value at which the distribution function is evaluated
    
    Returns:
    distribution function evaluated at x
  - barF
```
public double barF(double x)
```
    Description copied from class: ContinuousDistribution
    
    Returns the complementary distribution function. The default implementation computes bar(F)(x) = 1 - F(x).
    
    Specified by:
    
    barF in interface Distribution
    
    Overrides:
    
    barF in class ContinuousDistribution
    
    Parameters:
    x - value at which the complementary distribution function is evaluated
    
    Returns:
    complementary distribution function evaluated at x
  - inverseF
```
public double inverseF(double u)
```
    Description copied from class: ContinuousDistribution
    
    Returns the inverse distribution function x = F^-1(u). Restrictions: u∈[0, 1].
    
    Specified by:
    
    inverseF in interface Distribution
    
    Overrides:
    
    inverseF in class ContinuousDistribution
    
    Parameters:
    u - value at which the inverse distribution function is evaluated
    
    Returns:
    the inverse distribution function evaluated at u
  - density
```
public static double density(int n,
             double x)
```
    Computes the density of the Kolmogorov-Smirnov+ distribution with parameter n.
  - cdf
```
public static double cdf(int n,
         double x)
```
    Computes the Kolmogorov-Smirnov+ distribution function F_n(x) with parameter n. The relative error on F_n(x) = P[D_n⁺ <= x] is always less than 10^-5.
  - barF
```
public static double barF(int n,
          double x)
```
    Computes the complementary distribution function bar(F)_n(x) with parameter n.
  - inverseF
```
public static double inverseF(int n,
              double u)
```
    Computes the inverse x = F^-1(u) of the distribution with parameter n.
  - getN
```
public int getN()
```
    Returns the parameter n of this object.
  - setN
```
public void setN(int n)
```
    Sets the parameter n of this object.
  - getParams
```
public double[] getParams()
```
    Returns an array containing the parameter n of this object.
  - toString
```
public java.lang.String toString()
```
    Overrides:
    
    toString in class java.lang.Object

D_n⁺	=	max_{1 <= j <= n}(j/n - U_(j)),
D_n^-	=	max_{1 <= j <= n}(U_(j) - (j - 1)/n),

Class KolmogorovSmirnovPlusDist

Field Summary

Fields inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution

Constructor Summary

Method Summary

Methods inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution

Methods inherited from class java.lang.Object

Constructor Detail

KolmogorovSmirnovPlusDist

Method Detail

density

cdf

barF

inverseF

density

cdf

barF

inverseF

getN

setN

getParams

toString