umontreal.iro.lecuyer.probdist
Class ChiDist

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

All Implemented Interfaces:

Distribution

public class ChiDist
extends ContinuousDistribution

Extends the class ContinuousDistribution for the chi distribution with shape parameter v > 0. The density function is given by

f (x) = e^-x2/2x^v-1/(2^(v/2)-1Γ(v/2)) for x > 0,

where Γ(x) is the gamma function defined in GammaDist. The distribution function is

F(x) = 1/Γ(v/2)∫₀^x2/2t^v/2-1e^-t dt.

It is equivalent to the gamma distribution function with parameters α = v/2 and λ = 1, evaluated at x²/2.

Field Summary

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

decPrec

Constructor Summary

ChiDist(int nu)
Constructs an ChiDist object.

Method Summary

double	barF(double x) Returns bar(F)(x) = 1 - F(x).
static double	barF(int nu, double x) Computes the complementary distribution.
double	cdf(double x) Computes and returns the distribution function F(x).
static double	cdf(int nu, double x) Computes the distribution function by using the gamma distribution function.
double	density(double x) Returns f (x), the density of X evaluated at x.
static double	density(int nu, double x) Computes the density function.
int	getNu() Returns the value of ν for this object.
double	inverseF(double u) Computes and returns the inverse distribution function F-1(u), defined in.
static double	inverseF(int nu, double u) Returns the inverse distribution function computed using the gamma inversion.
void	setNu(int nu) Sets the value of ν for 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

ChiDist

public ChiDist(int nu)

Constructs an ChiDist object.

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 nu,
                             double x)

Computes the density function.

cdf

public static double cdf(int nu,
                         double x)

Computes the distribution function by using the gamma distribution function.

barF

public static double barF(int nu,
                          double x)

Computes the complementary distribution.

inverseF

public static double inverseF(int nu,
                              double u)

Returns the inverse distribution function computed using the gamma inversion.

getNu

public int getNu()

Returns the value of ν for this object.

setNu

public void setNu(int nu)

Sets the value of ν for this object.