umontreal.iro.lecuyer.probdist
Class AndersonDarlingDistQuick

java.lang.Object
  umontreal.iro.lecuyer.probdist.ContinuousDistribution
      umontreal.iro.lecuyer.probdist.AndersonDarlingDist
          umontreal.iro.lecuyer.probdist.AndersonDarlingDistQuick

All Implemented Interfaces:

Distribution

public class AndersonDarlingDistQuick
extends AndersonDarlingDist

Extends the class AndersonDarlingDist for the distribution (see). This class implements a version faster and more precise in the tails than class AndersonDarlingDist.

Field Summary

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

decPrec

Constructor Summary

AndersonDarlingDistQuick(int n)
Constructs an 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 distribution function Fn(x) at x for sample size 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 distribution with parameter n.
double	inverseF(double u) Returns the inverse distribution function x = F-1(u).
static double	inverseF(int n, double u) Computes the inverse x = Fn-1(u) of the distribution with parameter n.
String	toString()

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

getN, getParams, setN

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

AndersonDarlingDistQuick

public AndersonDarlingDistQuick(int n)

Constructs an 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.

Overrides:

density in class AndersonDarlingDist

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).

Specified by:

cdf in interface Distribution

Overrides:

cdf in class AndersonDarlingDist

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 AndersonDarlingDist

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 AndersonDarlingDist

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 distribution with parameter n.

cdf

public static double cdf(int n,
                         double x)

Computes the distribution function F_n(x) at x for sample size n. For 0.2 < x < 5, the asymptotic distribution F_∞(x) = lim_{n -> ∞}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 is used. For x < 0.2, the Marsaglias' approximation for n = ∞ is used.

For n > 6, the method gives at least 3 decimal digits of precision except for small x; for n <= 6, it gives at least 2 decimal digits of precision except for small x. For n = 1, the exact formula F₁(x) = (1 - 4e^-x-1)^1/2, for x >= ln(4) - 1, is used.

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_n^-1(u) of the distribution with parameter n.

toString

public String toString()

Overrides:

toString in class AndersonDarlingDist