SSJ  3.3.1
Stochastic Simulation in Java
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AndersonDarlingDist Class Reference

Extends the class ContinuousDistribution for the Anderson–Darling distribution (see [6], [165], [173], [225] ). More...

Inheritance diagram for AndersonDarlingDist:
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Collaboration diagram for AndersonDarlingDist:
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Public Member Functions

 AndersonDarlingDist (int n)
 Constructs an Anderson–Darling distribution for a sample of size \(n\).
 
double density (double x)
 
double cdf (double x)
 Returns the distribution function \(F(x)\). More...
 
double barF (double x)
 Returns \(\bar{F}(x) = 1 - F(x)\). More...
 
double inverseF (double u)
 Returns the inverse distribution function \(F^{-1}(u)\), defined in ( inverseF ). More...
 
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 ContinuousDistribution
abstract double density (double x)
 Returns \(f(x)\), the density evaluated at \(x\). More...
 
double barF (double x)
 Returns the complementary distribution function. More...
 
double inverseBrent (double a, double b, double u, double tol)
 Computes the inverse distribution function \(x = F^{-1}(u)\), using the Brent-Dekker method. More...
 
double inverseBisection (double u)
 Computes and returns the inverse distribution function \(x = F^{-1}(u)\), using bisection. More...
 
double inverseF (double u)
 Returns the inverse distribution function \(x = F^{-1}(u)\). More...
 
double getMean ()
 Returns the mean. More...
 
double getVariance ()
 Returns the variance. More...
 
double getStandardDeviation ()
 Returns the standard deviation. More...
 
double getXinf ()
 Returns \(x_a\) such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\). More...
 
double getXsup ()
 Returns \(x_b\) such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\). More...
 
void setXinf (double xa)
 Sets the value \(x_a=\) xa, such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\). More...
 
void setXsup (double xb)
 Sets the value \(x_b=\) xb, such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\). More...
 

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. More...
 
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 \(n\).
 

Static Protected Member Functions

static double density_N_1 (double x)
 
static double cdf_N_1 (double x)
 
static double barF_N_1 (double x)
 
static double inverse_N_1 (double u)
 

Protected Attributes

int n
 
- Protected Attributes inherited from ContinuousDistribution
double supportA = Double.NEGATIVE_INFINITY
 
double supportB = Double.POSITIVE_INFINITY
 

Additional Inherited Members

- Public Attributes inherited from ContinuousDistribution
int decPrec = 15
 
- Static Protected Attributes inherited from ContinuousDistribution
static final double XBIG = 100.0
 
static final double XBIGM = 1000.0
 
static final double [] EPSARRAY
 

Detailed Description

Extends the class ContinuousDistribution for the Anderson–Darling distribution (see [6], [165], [173], [225] ).

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 \(F_n(x) = P[A_n^2 \le x]\).

Member Function Documentation

◆ barF()

double barF ( double  x)

Returns \(\bar{F}(x) = 1 - F(x)\).

Parameters
xvalue at which the complementary distribution function is evaluated
Returns
complementary distribution function evaluated at x

Implements Distribution.

◆ cdf() [1/2]

double cdf ( double  x)

Returns the distribution function \(F(x)\).

Parameters
xvalue at which the distribution function is evaluated
Returns
distribution function evaluated at x

Implements Distribution.

◆ cdf() [2/2]

static double cdf ( int  n,
double  x 
)
static

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

algorithm [173] . First the asymptotic distribution for \(n\to\infty\) is computed. Then an empirical correction obtained by simulation is added for finite \(n\).

◆ inverseF()

double inverseF ( double  u)

Returns the inverse distribution function \(F^{-1}(u)\), defined in ( inverseF ).

Parameters
uvalue in the interval \((0,1)\) for which the inverse distribution function is evaluated
Returns
the inverse distribution function evaluated at u

Implements Distribution.


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