umontreal.iro.lecuyer.probdist

Class TruncatedDist

java.lang.Object

umontreal.iro.lecuyer.probdist.ContinuousDistribution

umontreal.iro.lecuyer.probdist.TruncatedDist

All Implemented Interfaces:

Distribution

public class TruncatedDist
extends ContinuousDistribution

This container class takes an arbitrary continuous distribution and truncates it to an interval [a, b], where a and b can be finite or infinite. If the original density and distribution function are f₀ and F₀, the new ones are f and F, defined by

f (x) = f₀(x)/(F₀(b) - F₀(a)) for a <= x <= b

and f (x) = 0 elsewhere, and

F(x) = (F₀(x) - F₀(a))/(F₀(b) - F₀(a)) for a <= x <= b.

The inverse distribution function of the truncated distribution is

F^-1(u) = F₀^-1(F₀(a) + (F₀(b) - F₀(a))u)

where F₀^-1 is the inverse distribution function of the original distribution.

Field Summary

Fields

Modifier and Type	Field and Description
static int	NUMINTERVALS

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

decPrec

Constructor Summary

Constructors

Constructor and Description
TruncatedDist(ContinuousDistribution dist, double a, double b) Constructs a new distribution by truncating distribution dist to the interval [a, b].

Method Summary

Modifier and Type	Method and Description
double	barF(double x) Returns the complementary distribution function.
double	cdf(double x) Returns the distribution function F(x).
double	density(double x) Returns f (x), the density evaluated at x.
double	getA() Returns the value of a.
double	getArea() Returns the value of F0(b) - F0(a), the area under the truncated density function.
double	getB() Returns the value of b.
double	getFa() Returns the value of F0(a).
double	getFb() Returns the value of F0(b).
double	getMean() Returns an approximation of the mean computed with the Simpson 1/3 numerical integration rule.
double[]	getParams() Return a table containing the parameters of the current distribution.
double	getStandardDeviation() Returns the square root of the approximate variance.
double	getVariance() Returns an approximation of the variance computed with the Simpson 1/3 numerical integration rule.
double	inverseF(double u) Returns the inverse distribution function x = F-1(u).
void	setParams(ContinuousDistribution dist, double a, double b) Sets the parameters dist, a and b for this object.
java.lang.String	toString() Returns a String containing information about the current distribution.

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

getXinf, getXsup, inverseBisection, inverseBrent, setXinf, setXsup

Methods inherited from class java.lang.Object

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

Field Detail

NUMINTERVALS

public static int NUMINTERVALS

Constructor Detail

TruncatedDist

public TruncatedDist(ContinuousDistribution dist,
                     double a,
                     double b)

Constructs a new distribution by truncating distribution dist to the interval [a, b]. Restrictions: a and b must be finite.

Method Detail

density

public double density(double x)

Description copied from class: ContinuousDistribution

Returns f (x), the density 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

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 class: ContinuousDistribution

Returns the complementary distribution function. The default implementation computes 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 class: ContinuousDistribution

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

Specified by:

inverseF in interface Distribution

Overrides:

inverseF in class ContinuousDistribution

Parameters:

u - value at which the inverse distribution function is evaluated

Returns:

the inverse distribution function evaluated at u

getMean

public double getMean()

Returns an approximation of the mean computed with the Simpson 1/3 numerical integration rule.

Specified by:

getMean in interface Distribution

Overrides:

getMean in class ContinuousDistribution

Returns:

the mean

Throws:

java.lang.UnsupportedOperationException - the mean of the truncated distribution is unknown

getVariance

public double getVariance()

Returns an approximation of the variance computed with the Simpson 1/3 numerical integration rule.

Specified by:

getVariance in interface Distribution

Overrides:

getVariance in class ContinuousDistribution

Returns:

the variance

Throws:

java.lang.UnsupportedOperationException - the mean of the truncated distribution is unknown

getStandardDeviation

public double getStandardDeviation()

Returns the square root of the approximate variance.

Specified by:

getStandardDeviation in interface Distribution

Overrides:

getStandardDeviation in class ContinuousDistribution

Returns:

the standard deviation

Throws:

java.lang.UnsupportedOperationException - the mean of the truncated distribution is unknown

getA

public double getA()

Returns the value of a.

getB

public double getB()

Returns the value of b.

getFa

public double getFa()

Returns the value of F₀(a).

getFb

public double getFb()

Returns the value of F₀(b).

getArea

public double getArea()

Returns the value of F₀(b) - F₀(a), the area under the truncated density function.

setParams

public void setParams(ContinuousDistribution dist,
                      double a,
                      double b)

Sets the parameters dist, a and b for this object. See the constructor for details.

getParams

public double[] getParams()

Return a table containing the parameters of the current distribution. This table is put in order: [a, b, F₀(a), F₀(b), F₀(b) - F₀(a)].

toString

public java.lang.String toString()

Returns a String containing information about the current distribution.

Overrides:

toString in class java.lang.Object