Extends the class ContinuousDistribution for the Anderson–Darling distribution (see [6], [161], [169],. More...

Inheritance diagram for umontreal.ssj.probdist.AndersonDarlingDist:

Public Member Functions
	AndersonDarlingDist (int n)
	Constructs an Anderson–Darling distribution for a sample of size \(n\).
double	density (double x)
	Returns \(f(x)\), the density evaluated at \(x\).
double	cdf (double x)
	Returns the distribution function \(F(x)\).
double	barF (double x)
	Returns the complementary distribution function.
double	inverseF (double u)
	Returns the inverse distribution function \(x = F^{-1}(u)\).
int	getN ()
	Returns the parameter \(n\) of this object.
void	setN (int n)
	Sets the parameter \(n\) of this object.
double[]	getParams ()
	Return an array containing the parameter \(n\) of the current distribution.
String	toString ()
	Returns a String containing information about the current distribution.
Public Member Functions inherited from umontreal.ssj.probdist.ContinuousDistribution
double	inverseBrent (double a, double b, double u, double tol)
	Computes the inverse distribution function \(x = F^{-1}(u)\), using the Brent-Dekker method.
double	inverseBisection (double u)
	Computes and returns the inverse distribution function \(x = F^{-1}(u)\), using bisection.
double	getMean ()
	Returns the mean.
double	getVariance ()
	Returns the variance.
double	getStandardDeviation ()
	Returns the standard deviation.
double	getXinf ()
	Returns \(x_a\) such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\).
double	getXsup ()
	Returns \(x_b\) such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\).
void	setXinf (double xa)
	Sets the value \(x_a=\) xa, such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\).
void	setXsup (double xb)
	Sets the value \(x_b=\) xb, such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\).

Static Public Member Functions
static double	density (int n, double x)
	Computes the density of the Anderson–Darling distribution with parameter \(n\).
static double	cdf (int n, double x)
	Computes the Anderson–Darling distribution function \(F_n(x)\), with parameter \(n\), using Marsaglia’s and al.
static double	barF (int n, double x)
	Computes the complementary distribution function \(\bar{F}_n(x)\) with parameter \(n\).
static double	inverseF (int n, double u)
	Computes the inverse \(x = F_n^{-1}(u)\) of the Anderson–Darling distribution with parameter \(n\).

Detailed Description

Extends the class ContinuousDistribution for the Anderson–Darling distribution (see [6], [161], [169],.

[216] ). Given a sample of \(n\) independent uniforms \(U_i\) over \((0,1)\), the Anderson–Darling statistic \(A_n^2\) is defined by

\begin{align*} A_n^2 & = -n -\frac{1}{n} \sum_{j=1}^n \left\{ (2j-1)\ln(U_{(j)}) + (2n+1-2j) \ln(1-U_{(j)}) \right\}, \tag{Andar} \end{align*}

where the \(U_{(j)}\) are the \(U_i\) sorted in increasing order. The distribution function (the cumulative probabilities) is defined as \(F_n(x) = P[A_n^2 \le x]\).

Definition at line 48 of file AndersonDarlingDist.java.

Constructor & Destructor Documentation

◆ AndersonDarlingDist()

umontreal.ssj.probdist.AndersonDarlingDist.AndersonDarlingDist ( int n )

Constructs an Anderson–Darling distribution for a sample of size \(n\).

Definition at line 68 of file AndersonDarlingDist.java.

Member Function Documentation

◆ barF() [1/2]

double umontreal.ssj.probdist.AndersonDarlingDist.barF ( double x )

Returns the complementary distribution function.

The default implementation computes \(\bar{F}(x) = 1 - F(x)\).

Parameters

x	value at which the complementary distribution function is evaluated

Returns: complementary distribution function evaluated at x

Reimplemented from umontreal.ssj.probdist.ContinuousDistribution.

Reimplemented in umontreal.ssj.probdist.AndersonDarlingDistQuick.

Definition at line 80 of file AndersonDarlingDist.java.

◆ barF() [2/2]

double umontreal.ssj.probdist.AndersonDarlingDist.barF	(	int	n,
		double	x )

static

Computes the complementary distribution function \(\bar{F}_n(x)\) with parameter \(n\).

Reimplemented in umontreal.ssj.probdist.AndersonDarlingDistQuick.

Definition at line 257 of file AndersonDarlingDist.java.

◆ cdf() [1/2]

double umontreal.ssj.probdist.AndersonDarlingDist.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 umontreal.ssj.probdist.Distribution.

Reimplemented in umontreal.ssj.probdist.AndersonDarlingDistQuick.

Definition at line 76 of file AndersonDarlingDist.java.

◆ cdf() [2/2]

double umontreal.ssj.probdist.AndersonDarlingDist.cdf	(	int	n,
		double	x )

static

Computes the Anderson–Darling distribution function \(F_n(x)\), with parameter \(n\), using Marsaglia’s and al.

algorithm

[169] . First the asymptotic distribution for \(n\to\infty\) is computed. Then an empirical correction obtained by simulation is added for finite \(n\).

Reimplemented in umontreal.ssj.probdist.AndersonDarlingDistQuick.

Definition at line 223 of file AndersonDarlingDist.java.

◆ density() [1/2]

double umontreal.ssj.probdist.AndersonDarlingDist.density ( double x )

Returns \(f(x)\), the density evaluated at \(x\).

Parameters

x	value at which the density is evaluated

Returns: density function evaluated at x

Reimplemented from umontreal.ssj.probdist.ContinuousDistribution.

Reimplemented in umontreal.ssj.probdist.AndersonDarlingDistQuick.

Definition at line 72 of file AndersonDarlingDist.java.

◆ density() [2/2]

double umontreal.ssj.probdist.AndersonDarlingDist.density	(	int	n,
		double	x )

static

Computes the density of the Anderson–Darling distribution with parameter \(n\).

Reimplemented in umontreal.ssj.probdist.AndersonDarlingDistQuick.

Definition at line 106 of file AndersonDarlingDist.java.

◆ getN()

int umontreal.ssj.probdist.AndersonDarlingDist.getN ( )

Returns the parameter \(n\) of this object.

Definition at line 297 of file AndersonDarlingDist.java.

◆ getParams()

double[] umontreal.ssj.probdist.AndersonDarlingDist.getParams ( )

Return an array containing the parameter \(n\) of the current distribution.

Implements umontreal.ssj.probdist.Distribution.

Definition at line 320 of file AndersonDarlingDist.java.

◆ inverseF() [1/2]

double umontreal.ssj.probdist.AndersonDarlingDist.inverseF ( double u )

Returns the inverse distribution function \(x = F^{-1}(u)\).

Restrictions: \(u \in[0,1]\).

Parameters

u	value at which the inverse distribution function is evaluated

Returns: the inverse distribution function evaluated at u

Exceptions

IllegalArgumentException if \(u\) is not in the interval \([0,1]\)

Reimplemented from umontreal.ssj.probdist.ContinuousDistribution.

Reimplemented in umontreal.ssj.probdist.AndersonDarlingDistQuick.

Definition at line 84 of file AndersonDarlingDist.java.

◆ inverseF() [2/2]

double umontreal.ssj.probdist.AndersonDarlingDist.inverseF	(	int	n,
		double	u )

static

Computes the inverse \(x = F_n^{-1}(u)\) of the Anderson–Darling distribution with parameter \(n\).

Reimplemented in umontreal.ssj.probdist.AndersonDarlingDistQuick.

Definition at line 279 of file AndersonDarlingDist.java.

◆ setN()

void umontreal.ssj.probdist.AndersonDarlingDist.setN ( int n )

Sets the parameter \(n\) of this object.

Definition at line 304 of file AndersonDarlingDist.java.

◆ toString()

String umontreal.ssj.probdist.AndersonDarlingDist.toString ( )

Returns a String containing information about the current distribution.

Reimplemented in umontreal.ssj.probdist.AndersonDarlingDistQuick.

Definition at line 328 of file AndersonDarlingDist.java.

The documentation for this class was generated from the following file:

src/main/java/umontreal/ssj/probdist/AndersonDarlingDist.java

SSJ API Documentation Stochastic Simulation in Java

Public Member Functions

Static Public Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ AndersonDarlingDist()

Member Function Documentation

◆ barF() [1/2]

◆ barF() [2/2]

◆ cdf() [1/2]

◆ cdf() [2/2]

◆ density() [1/2]

◆ density() [2/2]

◆ getN()

◆ getParams()

◆ inverseF() [1/2]

◆ inverseF() [2/2]

◆ setN()

◆ toString()