umontreal.iro.lecuyer.probdist
Class ChiSquareDist

java.lang.Object
  umontreal.iro.lecuyer.probdist.ContinuousDistribution
      umontreal.iro.lecuyer.probdist.ChiSquareDist

All Implemented Interfaces:

Distribution

Direct Known Subclasses:

ChiSquareDistQuick

public class ChiSquareDist
extends ContinuousDistribution

Extends the class ContinuousDistribution for the chi-square distribution with n degrees of freedom, where n is a positive integer. Its density is

f (x) = x^(n/2)-1e^-x/2/(2^n/2Γ(n/2)), for x > 0.

where Γ(x) is the gamma function defined in GammaDist. The chi-square distribution is a special case of the gamma distribution with shape parameter n/2 and scale parameter 1/2. Therefore, one can use the methods of GammaDist for this distribution.

The non-static versions of the methods cdf, barF, and inverseF call the static version of the same name.

Field Summary

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

decPrec

Constructor Summary

ChiSquareDist(int n)
Constructs a chi-square distribution with n degrees of freedom.

Method Summary

double	barF(double x) Returns bar(F)(x) = 1 - F(x).
static double	barF(int n, int d, double x) Computes the complementary chi-square distribution function with n degrees of freedom.
double	cdf(double x) Computes and returns the distribution function F(x).
static double	cdf(int n, int d, double x) Computes an approximation of the chi-square distribution function with n degrees of freedom.
double	density(double x) Returns f (x), the density of X evaluated at x.
static double	density(int n, double x) Computes the density function for a chi-square distribution with n degrees of freedom.
int	getN() Returns the parameter n of this object.
double	inverseF(double u) Computes and returns the inverse distribution function F-1(u), defined in.
static double	inverseF(int n, double u) Computes an approximation of F-1(u), where F is the chi-square distribution with n degrees of freedom.
void	setN(int n) Sets the parameter n of this object.

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

inverseBisection, inverseBrent

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

ChiSquareDist

public ChiSquareDist(int n)

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

Method Detail

density

public double density(double x)

Description copied from class: ContinuousDistribution

Returns f (x), the density of X evaluated at x.

Specified by:

density in class ContinuousDistribution

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

Computes and returns the distribution function F(x).

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 interface: Distribution

Returns bar(F)(x) = 1 - F(x).

Specified by:

barF in interface Distribution

Overrides:

barF in class ContinuousDistribution

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 interface: Distribution

Computes and returns the inverse distribution function F^-1(u), defined in.

Specified by:

inverseF in interface Distribution

Overrides:

inverseF in class ContinuousDistribution

Parameters:

u - value in the interval (0, 1) for 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 function for a chi-square distribution with n degrees of freedom.

cdf

public static double cdf(int n,
                         int d,
                         double x)

Computes an approximation of the chi-square distribution function with n degrees of freedom. Uses the approximation given by Kennedy and Gentle (1980) for n <= 350 (which gives nearly 12 decimal digits of precision for 10^-5 < u < 1 - 10^-5). For n > 350, this implementation invokes the method GammaDist.cdf (n/2, d, x/2) instead, because it is faster and as accurate as the above approximation for such n.

barF

public static double barF(int n,
                          int d,
                          double x)

Computes the complementary chi-square distribution function with n degrees of freedom. Uses the approximation given by Kennedy and Gentle for n <= 350, and invokes the method GammaDist.barF (n/2, d, x/2) for n > 350.

inverseF

public static double inverseF(int n,
                              double u)

Computes an approximation of F^-1(u), where F is the chi-square distribution with n degrees of freedom. It gives at least 6 decimal digits of precision, except far in the tails (that is, for u < 10^-5 or u > 1 - 10^-5) where the function calls the method GammaDist.inverseF (n/2, 7, u) and multiplies the result by 2.0. To get better precision, one may call GammaDist.inverseF, but this method is slower than the current method, especially for large n. For instance, for n = 16, 1024, and 65536, the GammaDist.inverseF method is 2, 5, and 8 times slower, respectively, than the current method.

getN

public int getN()

Returns the parameter n of this object.

setN

public void setN(int n)

Sets the parameter n of this object.