Extends the class AndersonDarlingDist for the Anderson–Darling distribution (see [6], [161], [216] ). More...

Inheritance diagram for umontreal.ssj.probdist.AndersonDarlingDistQuick:

Public Member Functions
	AndersonDarlingDistQuick (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 \(x = F^{-1}(u)\).
String	toString ()
	Returns a String containing information about the current distribution.
Public Member Functions inherited from umontreal.ssj.probdist.AndersonDarlingDist
	AndersonDarlingDist (int n)
	Constructs an Anderson–Darling distribution for a sample of size \(n\).
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.
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 \(F_n(x)\) at.
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 AndersonDarlingDist for the Anderson–Darling distribution (see [6], [161], [216] ).

This class implements a version faster and more precise in the tails than class AndersonDarlingDist.

Definition at line 40 of file AndersonDarlingDistQuick.java.

Constructor & Destructor Documentation

◆ AndersonDarlingDistQuick()

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

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

Definition at line 73 of file AndersonDarlingDistQuick.java.

Member Function Documentation

◆ barF() [1/2]

double umontreal.ssj.probdist.AndersonDarlingDistQuick.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.AndersonDarlingDist.

Definition at line 85 of file AndersonDarlingDistQuick.java.

◆ barF() [2/2]

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

static

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

Reimplemented from umontreal.ssj.probdist.AndersonDarlingDist.

Definition at line 361 of file AndersonDarlingDistQuick.java.

◆ cdf() [1/2]

double umontreal.ssj.probdist.AndersonDarlingDistQuick.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

Reimplemented from umontreal.ssj.probdist.AndersonDarlingDist.

Definition at line 81 of file AndersonDarlingDistQuick.java.

◆ cdf() [2/2]

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

static

Computes the Anderson–Darling distribution function \(F_n(x)\) at.

\(x\) for sample size \(n\). For \(0.2 < x < 5\), the asymptotic distribution \(F_{\infty}(x) = \lim_{n\to\infty} F_n(x)\) was first computed by numerical integration; then a linear correction \(O(1/n)\) obtained by simulation was added. For \(5 < x\), the Grace-Wood empirical approximation [72] is used. For \(x < 0.2\), the Marsaglias’ approximation [169] for \(n=\infty\) is used.

For \(n>6\), the method gives at least 3 decimal digits of precision except for small \(x\); for \(n \le6\), it gives at least 2 decimal digits of precision except for small \(x\). For \(n=1\), the exact formula \(F_1(x) = \sqrt{1 - 4e^{-x-1}}\), for \(x\ge\ln(4) - 1\), is used.

Reimplemented from umontreal.ssj.probdist.AndersonDarlingDist.

Definition at line 343 of file AndersonDarlingDistQuick.java.