Provides a variant of ChiSquareDist with faster but less accurate methods. More...

Inheritance diagram for umontreal.ssj.probdist.ChiSquareDistQuick:

Public Member Functions
	ChiSquareDistQuick (int n)
	Constructs a chi-square distribution with n degrees of freedom.
double	inverseF (double u)
	Returns the inverse distribution function \(x = F^{-1}(u)\).
Public Member Functions inherited from umontreal.ssj.probdist.ChiSquareDist
	ChiSquareDist (int n)
	Constructs a chi-square distribution with n degrees of freedom.
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	getMean ()
	Returns the mean.
double	getVariance ()
	Returns the variance.
double	getStandardDeviation ()
	Returns the standard deviation.
int	getN ()
	Returns the parameter \(n\) of this object.
void	setN (int n)
	Sets the parameter \(n\) of this object.
double[]	getParams ()
	Return a table containing the parameters 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	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	inverseF (int n, double u)
	Computes a quick-and-dirty approximation of \(F^{-1}(u)\), where \(F\) is the chi-square distribution with \(n\) degrees of freedom.
Static Public Member Functions inherited from umontreal.ssj.probdist.ChiSquareDist
static double	density (int n, double x)
	Computes the density function ( `Fchi2` ) for a chi-square distribution with \(n\) degrees of freedom.
static double	cdf (int n, int d, double x)
	Computes the chi-square distribution function with \(n\) degrees of freedom, evaluated at \(x\).
static double	barF (int n, int d, double x)
	Computes the complementary chi-square distribution function with.
static double[]	getMLE (double[] x, int m)
	Estimates the parameter \(n\) of the chi-square distribution using the maximum likelihood method, from the \(m\) observations.
static ChiSquareDist	getInstanceFromMLE (double[] x, int m)
	Creates a new instance of a chi-square distribution with parameter.
static double	getMean (int n)
	Computes and returns the mean \(E[X] = n\) of the chi-square distribution with parameter \(n\).
static double[]	getMomentsEstimate (double[] x, int m)
	Estimates and returns the parameter [ \(\hat{n}\)] of the chi-square distribution using the moments method based on the.
static double	getVariance (int n)
	Returns the variance \(\mbox{Var}[X] = 2n\) of the chi-square distribution with parameter \(n\).
static double	getStandardDeviation (int n)
	Returns the standard deviation of the chi-square distribution with parameter \(n\).

Detailed Description

Provides a variant of ChiSquareDist with faster but less accurate methods.

The non-static version of inverseF calls the static version. This method is not very accurate for small \(n\) but becomes better as

\(n\) increases. The other methods are the same as in ChiSquareDist.

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Definition at line 39 of file ChiSquareDistQuick.java.

Constructor & Destructor Documentation

◆ ChiSquareDistQuick()

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

Constructs a chi-square distribution with n degrees of freedom.

Definition at line 44 of file ChiSquareDistQuick.java.

Member Function Documentation

◆ inverseF() [1/2]

double umontreal.ssj.probdist.ChiSquareDistQuick.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.ChiSquareDist.

Definition at line 48 of file ChiSquareDistQuick.java.

◆ inverseF() [2/2]

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

static

Computes a quick-and-dirty approximation of \(F^{-1}(u)\), where \(F\) is the chi-square distribution with \(n\) degrees of freedom.

Uses the approximation given in Figure L.24 of [24] over most of the range. For \(u < 0.02\) or \(u > 0.98\), it uses the approximation given in [71] for \(n \ge10\), and returns 2.0 * inverseF(n/2, 6, u) for \(n < 10\) in order to avoid the loss of precision of the above approximations. When \(n \ge10\) or \(0.02 < u < 0.98\), it is between 20 to 30 times faster than the same method in ChiSquareDist for \(n\) between \(10\) and \(1000\) and even faster for larger

\(n\).

     Note that the number @f$d@f$ of decimal digits of precision
     generally increases with @f$n@f$. For @f$n=3@f$, we only have @f$d =
     3@f$ over most of the range. For @f$n=10@f$, @f$d=5@f$ except far in
     the tails where @f$d = 3@f$. For @f$n=100@f$, one has more
     than @f$d=7@f$ over most of the range and for @f$n=1000@f$, at
     least @f$d=8@f$. The cases @f$n = 1@f$ and

\(n = 2\) are exceptions, with precision of about \(d=10\).

Reimplemented from umontreal.ssj.probdist.ChiSquareDist.

Definition at line 74 of file ChiSquareDistQuick.java.

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

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

SSJ API Documentation Stochastic Simulation in Java