SSJ
V. 2.6.

## umontreal.iro.lecuyer.probdist Class WatsonGDist

```java.lang.Object
umontreal.iro.lecuyer.probdist.ContinuousDistribution
umontreal.iro.lecuyer.probdist.WatsonGDist
```
All Implemented Interfaces:
Distribution

`public class WatsonGDistextends ContinuousDistribution`

Extends the class `ContinuousDistribution` for the Watson G distribution (see). Given a sample of n independent uniforms Ui over [0, 1], the G statistic is defined by

 Gn = (n)1/2max1 <= j <= n{j/n - U(j) + bar(U)n -1/2} = (n)1/2(Dn+ + bar(U)n - 1/2),

where the U(j) are the Ui sorted in increasing order, bar(U)n is the average of the observations Ui, and Dn+ is the Kolmogorov-Smirnov+ statistic. The distribution function (the cumulative probabilities) is defined as Fn(x) = P[Gn <= x].

Field Summary

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

Constructor Summary
`WatsonGDist(int n)`
Constructs a Watson distribution for a sample of size 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)n(x) with parameter n.
` double` `cdf(double x)`
Returns the distribution function F(x).
`static double` ```cdf(int n, double x)```
Computes the Watson G distribution function Fn(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 function for a Watson G distribution with parameter n.
` int` `getN()`
Returns the parameter n of this object.
` double[]` `getParams()`
Return 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 x = Fn-1(u), where Fn is the Watson G distribution 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

### WatsonGDist

`public WatsonGDist(int n)`
Constructs a Watson 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 function for a Watson G distribution with parameter n.

### cdf

```public static double cdf(int n,
double x)```
Computes the Watson G distribution function Fn(x), with parameter n. A cubic spline interpolation is used for the asymptotic distribution when n -> ∞, and an empirical correction of order 1/(n)1/2, obtained empirically from 107 simulation runs with n = 256 is then added. The absolute error is estimated to be less than 0.01, 0.005, 0.002, 0.0008, 0.0005, 0.0005, 0.0005 for n = 16, 32, 64, 128, 256, 512, 1024, respectively.

### 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 x = Fn-1(u), where Fn is the Watson G 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()`
Return 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.