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. More...

Inheritance diagram for umontreal.ssj.probdist.TruncatedDist:

Public Member Functions
	TruncatedDist (ContinuousDistribution dist, double a, double b)
	Constructs a new distribution by truncating distribution dist to the interval \([a,b]\).
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	inverseF (double u)
	Returns the inverse distribution function \(x = F^{-1}(u)\).
double	getMean ()
	Returns an approximation of the mean computed with the Simpson.
double	getVariance ()
	Returns an approximation of the variance computed with the Simpson.
double	getStandardDeviation ()
	Returns the square root of the approximate variance.
double	getA ()
	Returns the value of \(a\).
double	getB ()
	Returns the value of \(b\).
double	getFa ()
	Returns the value of \(F_0(a)\).
double	getFb ()
	Returns the value of \(F_0(b)\).
double	getArea ()
	Returns the value of \(F_0(b) - F_0(a)\), the area under the truncated density function.
void	setParams (ContinuousDistribution dist, double a, double b)
	Sets the parameters dist, \(a\) and \(b\) for 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 \([x_a, x_b]\).

Detailed Description

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

\(f_0\) and \(F_0\), the new ones are \(f\) and \(F\), defined by

\[ f(x) = \frac{f_0(x)}{F_0(b) - F_0(a)} \qquad\mbox{ for } a\le x\le b \]

and \(f(x)=0\) elsewhere, and

\[ F(x) = \frac{F_0(x)-F_0(a)}{F_0(b)-F_0(a)} \qquad\mbox{ for } a\le x\le b. \]

The inverse distribution function of the truncated distribution is

\[ {F^{-1}}(u) = F_0^{-1}(F_0(a) + (F_0(b) - F_0(a))u) \]

where \(F_0^{-1}\) is the inverse distribution function of the original distribution.

Definition at line 48 of file TruncatedDist.java.

Constructor & Destructor Documentation

◆ TruncatedDist()

umontreal.ssj.probdist.TruncatedDist.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.

Definition at line 66 of file TruncatedDist.java.

Member Function Documentation

◆ barF()

double umontreal.ssj.probdist.TruncatedDist.barF ( double x )

Returns the complementary distribution function.

The default implementation computes \(\bar{F}(x) = 1 - F(x)\).

Parameters

x	value at which the complementary distribution function is evaluated

Returns: complementary distribution function evaluated at x

Reimplemented from umontreal.ssj.probdist.ContinuousDistribution.

Definition at line 85 of file TruncatedDist.java.

◆ cdf()

double umontreal.ssj.probdist.TruncatedDist.cdf ( double x )

Returns the distribution function \(F(x)\).

Parameters

x	value at which the distribution function is evaluated

Returns: distribution function evaluated at x

Implements umontreal.ssj.probdist.Distribution.

Definition at line 76 of file TruncatedDist.java.

◆ density()

double umontreal.ssj.probdist.TruncatedDist.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

Reimplemented from umontreal.ssj.probdist.ContinuousDistribution.

Definition at line 70 of file TruncatedDist.java.

◆ getA()

double umontreal.ssj.probdist.TruncatedDist.getA ( )

Returns the value of \(a\).

Definition at line 143 of file TruncatedDist.java.

◆ getArea()

double umontreal.ssj.probdist.TruncatedDist.getArea ( )

Returns the value of \(F_0(b) - F_0(a)\), the area under the truncated density function.

Definition at line 172 of file TruncatedDist.java.

◆ getB()

double umontreal.ssj.probdist.TruncatedDist.getB ( )

Returns the value of \(b\).

Definition at line 150 of file TruncatedDist.java.

◆ getFa()

double umontreal.ssj.probdist.TruncatedDist.getFa ( )

Returns the value of \(F_0(a)\).

Definition at line 157 of file TruncatedDist.java.

◆ getFb()

double umontreal.ssj.probdist.TruncatedDist.getFb ( )

Returns the value of \(F_0(b)\).

Definition at line 164 of file TruncatedDist.java.

◆ getMean()

double umontreal.ssj.probdist.TruncatedDist.getMean ( )

Returns an approximation of the mean computed with the Simpson.

\(1/3\) numerical integration rule.

Exceptions

UnsupportedOperationException the mean of the truncated distribution is unknown

Reimplemented from umontreal.ssj.probdist.ContinuousDistribution.

Definition at line 109 of file TruncatedDist.java.

◆ getParams()

double[] umontreal.ssj.probdist.TruncatedDist.getParams ( )

Return a table containing the parameters of the current distribution.

This table is put in order: [ \(a\), \(b\), \(F_0(a)\), \(F_0(b)\), \(F_0(b) - F_0(a)\)].

Implements umontreal.ssj.probdist.Distribution.

Definition at line 219 of file TruncatedDist.java.

◆ getStandardDeviation()

double umontreal.ssj.probdist.TruncatedDist.getStandardDeviation ( )

Returns the square root of the approximate variance.

Exceptions

UnsupportedOperationException the mean of the truncated distribution is unknown

Reimplemented from umontreal.ssj.probdist.ContinuousDistribution.

Definition at line 134 of file TruncatedDist.java.

◆ getVariance()

double umontreal.ssj.probdist.TruncatedDist.getVariance ( )

Returns an approximation of the variance computed with the Simpson.

\(1/3\) numerical integration rule.

Exceptions

UnsupportedOperationException the mean of the truncated distribution is unknown

Reimplemented from umontreal.ssj.probdist.ContinuousDistribution.

Definition at line 122 of file TruncatedDist.java.

◆ inverseF()

double umontreal.ssj.probdist.TruncatedDist.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.ContinuousDistribution.

Definition at line 94 of file TruncatedDist.java.

◆ setParams()

void umontreal.ssj.probdist.TruncatedDist.setParams	(	ContinuousDistribution	dist,
		double	a,
		double	b )

Sets the parameters dist, \(a\) and \(b\) for this object.

See the constructor for details.

Definition at line 180 of file TruncatedDist.java.

◆ toString()

String umontreal.ssj.probdist.TruncatedDist.toString ( )

Returns a String containing information about the current distribution.

Definition at line 227 of file TruncatedDist.java.

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

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

SSJ API Documentation Stochastic Simulation in Java

Public Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ TruncatedDist()

Member Function Documentation

◆ barF()

◆ cdf()

◆ density()

◆ getA()

◆ getArea()

◆ getB()

◆ getFa()

◆ getFb()

◆ getMean()

◆ getParams()

◆ getStandardDeviation()

◆ getVariance()

◆ inverseF()

◆ setParams()

◆ toString()