umontreal.iro.lecuyer.probdist

Class ContinuousDistribution

java.lang.Object

umontreal.iro.lecuyer.probdist.ContinuousDistribution

All Implemented Interfaces:

Distribution

Direct Known Subclasses:

AndersonDarlingDist, BetaDist, CauchyDist, ChiDist, ChiSquareDist, ChiSquareNoncentralDist, CramerVonMisesDist, ExponentialDist, ExtremeValueDist, FatigueLifeDist, FisherFDist, FoldedNormalDist, FrechetDist, GammaDist, GumbelDist, HalfNormalDist, HyperbolicSecantDist, InverseDistFromDensity, InverseGaussianDist, JohnsonSBDist, JohnsonSUDist, KolmogorovSmirnovDist, KolmogorovSmirnovPlusDist, LaplaceDist, LogisticDist, LoglogisticDist, LognormalDist, NakagamiDist, NormalDist, NormalInverseGaussianDist, ParetoDist, Pearson5Dist, Pearson6Dist, PiecewiseLinearEmpiricalDist, PowerDist, RayleighDist, StudentDist, TriangularDist, TruncatedDist, UniformDist, WatsonGDist, WatsonUDist, WeibullDist

public abstract class ContinuousDistribution
extends java.lang.Object
implements Distribution

Classes implementing continuous distributions should inherit from this base class. Such distributions are characterized by a density function f (x), thus the signature of a density method is supplied here. This class also provides default implementations for bar(F)(x) and for F^-1(u), the latter using the Brent-Dekker method to find the inverse of a generic distribution function F.

Field Summary

Fields

Modifier and Type	Field and Description
int	decPrec

Constructor Summary

Constructors

Constructor and Description
ContinuousDistribution()

Method Summary

Methods

Modifier and Type	Method and Description
double	barF(double x) Returns the complementary distribution function.
abstract double	density(double x) Returns f (x), the density evaluated at x.
double	getMean() Returns the mean.
double	getStandardDeviation() Returns the standard deviation.
double	getVariance() Returns the variance.
double	getXinf() Returns xa such that the probability density is 0 everywhere outside the interval [xa, xb].
double	getXsup() Returns xb such that the probability density is 0 everywhere outside the interval [xa, xb].
double	inverseBisection(double u) Computes and returns the inverse distribution function x = F-1(u), using bisection.
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	inverseF(double u) Returns the inverse distribution function x = F-1(u).
void	setXinf(double xa) Sets the value xa = xa, such that the probability density is 0 everywhere outside the interval [xa, xb].
void	setXsup(double xb) Sets the value xb = xb, such that the probability density is 0 everywhere outside the interval [xa, xb].

Methods inherited from class java.lang.Object

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

Methods inherited from interface umontreal.iro.lecuyer.probdist.Distribution

cdf, getParams

Field Detail

decPrec

public int decPrec

Constructor Detail

ContinuousDistribution

public ContinuousDistribution()

Method Detail

density

public abstract double density(double x)

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

Parameters:

x - value at which the density is evaluated

Returns:

density function evaluated at x

barF

public double barF(double x)

Returns the complementary distribution function. The default implementation computes bar(F)(x) = 1 - F(x).

Specified by:

barF in interface Distribution

Parameters:

x - value at which the complementary distribution function is evaluated

Returns:

complementary distribution function evaluated at x

inverseBrent

public double inverseBrent(double a,
                  double b,
                  double u,
                  double tol)

Computes the inverse distribution function x = F^-1(u), using the Brent-Dekker method. The interval [a, b] must contain the root x such that F(a) <= u <= F(b), where u = F(x). The calculations are done with an approximate precision of tol. Returns x = F^-1(u). Restrictions: u∈[0, 1].

Parameters:

a - left endpoint of initial interval

b - right endpoint of initial interval

u - value at which the inverse distribution function is evaluated

tol - accuracy goal

Returns:

inverse distribution function evaluated at u

inverseBisection

public double inverseBisection(double u)

Computes and returns the inverse distribution function x = F^-1(u), using bisection. Restrictions: u∈[0, 1].

Parameters:

u - value at which the inverse distribution function is evaluated

Returns:

the inverse distribution function evaluated at u

Throws:

java.lang.IllegalArgumentException - if u is not in the interval [0, 1]

inverseF

public double inverseF(double u)

Returns the inverse distribution function x = F^-1(u). Restrictions: u∈[0, 1].

Specified by:

inverseF in interface Distribution

Parameters:

u - value at which the inverse distribution function is evaluated

Returns:

the inverse distribution function evaluated at u

Throws:

java.lang.IllegalArgumentException - if u is not in the interval [0, 1]

getMean

public double getMean()

Returns the mean.

Specified by:

getMean in interface Distribution

Returns:

the mean

getVariance

public double getVariance()

Returns the variance.

Specified by:

getVariance in interface Distribution

Returns:

the variance

getStandardDeviation

public double getStandardDeviation()

Returns the standard deviation.

Specified by:

getStandardDeviation in interface Distribution

Returns:

the standard deviation

getXinf

public double getXinf()

Returns x_a such that the probability density is 0 everywhere outside the interval [x_a, x_b].

Returns:

lower limit of support

getXsup

public double getXsup()

Returns x_b such that the probability density is 0 everywhere outside the interval [x_a, x_b].

Returns:

upper limit of support

setXinf

public 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].

Parameters:

xa - lower limit of support

setXsup

public 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].

Parameters:

xb - upper limit of support