SSJ
V. 2.6.

## umontreal.iro.lecuyer.probdist Class KolmogorovSmirnovDist

```java.lang.Object
umontreal.iro.lecuyer.probdist.ContinuousDistribution
umontreal.iro.lecuyer.probdist.KolmogorovSmirnovDist
```
All Implemented Interfaces:
Distribution
Direct Known Subclasses:
KolmogorovSmirnovDistQuick

`public class KolmogorovSmirnovDistextends ContinuousDistribution`

Extends the class `ContinuousDistribution` for the Kolmogorov-Smirnov distribution with parameter n. Given an empirical distribution Fn with n independent observations and a continuous distribution F(x), the two-sided statistic is defined as

Dn = sup-∞ <= x <= ∞| Fn(x) - F(x)|  = {Dn+, Dn-},

where Dn+ and Dn- are the + and - statistics as defined in equations and on page of this guide. This class implements a high precision version of the distribution P[Dn <= x]; it is a Java translation of the C program written in. According to its authors, it should give 13 decimal digits of precision. It is extremely slow for large values of n.

Field Summary

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

Constructor Summary
`KolmogorovSmirnovDist(int n)`
Constructs a distribution with parameter n.

Method Summary
` double` `barF(double x)`
Returns the complementary distribution function.
`static double` ```barF(int n, double x)```
Computes the complementary distribution function bar(F)(x) with parameter n.
` double` `cdf(double x)`
Returns the distribution function F(x).
`static double` ```cdf(int n, double x)```
Computes the distribution function F(x) with parameter n using Durbin's matrix formula.
` double` `density(double x)`
Returns f (x), the density evaluated at x.
`static double` ```density(int n, double x)```
Computes the density for the 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 F(x) with parameter n.
` void` `setN(int n)`
Sets the parameter n of this object.
` 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

### KolmogorovSmirnovDist

`public KolmogorovSmirnovDist(int n)`
Constructs a distribution with parameter n. Restriction: n >= 1.

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 for the distribution with parameter n.

### cdf

```public static double cdf(int n,
double x)```
Computes the distribution function F(x) with parameter n using Durbin's matrix formula. It is a translation of the C program in; according to its authors, it returns 13 decimal digits of precision. It is extremely slow for large n.

### barF

```public static double barF(int n,
double x)```
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.

### inverseF

```public static double inverseF(int n,
double u)```
Computes the inverse x = F-1(u) of the distribution F(x) 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 String toString()`
Overrides:
`toString` in class `Object`

SSJ
V. 2.6.

To submit a bug or ask questions, send an e-mail to Pierre L'Ecuyer.