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 TruncatedDist:

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Collaboration diagram for TruncatedDist:

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Public Member Functions
	TruncatedDist (ContinuousDistribution dist, double a, double b)
	Constructs a new distribution by truncating distribution `dist` to the interval \([a,b]\). More...

double	density (double x)

double	cdf (double x)
	Returns the distribution function \(F(x)\). More...

double	barF (double x)
	Returns \(\bar{F}(x) = 1 - F(x)\). More...

double	inverseF (double u)
	Returns the inverse distribution function \(F^{-1}(u)\), defined in ( inverseF ). More...

double	getMean ()
	Returns an approximation of the mean computed with the Simpson \(1/3\) numerical integration rule. More...

double	getVariance ()
	Returns an approximation of the variance computed with the Simpson \(1/3\) numerical integration rule. More...

double	getStandardDeviation ()
	Returns the square root of the approximate variance. More...

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. More...

double []	getParams ()
	Return a table containing the parameters of the current distribution. More...

String	toString ()
	Returns a `String` containing information about the current distribution.

Public Member Functions inherited from ContinuousDistribution
abstract double	density (double x)
	Returns \(f(x)\), the density evaluated at \(x\). More...

double	barF (double x)
	Returns the complementary distribution function. More...

double	inverseBrent (double a, double b, double u, double tol)
	Computes the inverse distribution function \(x = F^{-1}(u)\), using the Brent-Dekker method. More...

double	inverseBisection (double u)
	Computes and returns the inverse distribution function \(x = F^{-1}(u)\), using bisection. More...

double	inverseF (double u)
	Returns the inverse distribution function \(x = F^{-1}(u)\). More...

double	getMean ()
	Returns the mean. More...

double	getVariance ()
	Returns the variance. More...

double	getStandardDeviation ()
	Returns the standard deviation. More...

double	getXinf ()
	Returns \(x_a\) such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\). More...

double	getXsup ()
	Returns \(x_b\) such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\). More...

void	setXinf (double xa)
	Sets the value \(x_a=\) `xa`, such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\). More...

void	setXsup (double xb)
	Sets the value \(x_b=\) `xb`, such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\). More...

Static Public Attributes
static int	NUMINTERVALS = 500

Additional Inherited Members
Public Attributes inherited from ContinuousDistribution
int	decPrec = 15

Protected Attributes inherited from ContinuousDistribution
double	supportA = Double.NEGATIVE_INFINITY

double	supportB = Double.POSITIVE_INFINITY

Static Protected Attributes inherited from ContinuousDistribution
static final double	XBIG = 100.0

static final double	XBIGM = 1000.0

static final double []	EPSARRAY

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.

Constructor & Destructor Documentation

◆ 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.

Member Function Documentation

◆ barF()

double barF ( double x )

Returns \(\bar{F}(x) = 1 - F(x)\).

Parameters

x	value at which the complementary distribution function is evaluated

Returns: complementary distribution function evaluated at x

Implements Distribution.

◆ cdf()

double 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 Distribution.

◆ getMean()

double 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

Implements Distribution.

◆ getParams()

double [] 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 Distribution.

◆ getStandardDeviation()

double getStandardDeviation ( )

Returns the square root of the approximate variance.

Exceptions

UnsupportedOperationException the mean of the truncated distribution is unknown

Implements Distribution.

◆ getVariance()

double 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

Implements Distribution.

◆ inverseF()

double inverseF ( double u )

Returns the inverse distribution function \(F^{-1}(u)\), defined in ( inverseF ).

Parameters

u	value in the interval \((0,1)\) for which the inverse distribution function is evaluated

Returns: the inverse distribution function evaluated at u

Implements Distribution.

◆ setParams()

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

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

See the constructor for details.

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

TruncatedDist.java

Public Member Functions

Static Public Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ TruncatedDist()

Member Function Documentation

◆ barF()

◆ cdf()

◆ getMean()

◆ getParams()

◆ getStandardDeviation()

◆ getVariance()

◆ inverseF()

◆ setParams()