Classes implementing continuous distributions should inherit from this base class. More...

Inheritance diagram for umontreal.ssj.probdist.ContinuousDistribution:

Public Member Functions
abstract double	density (double x)
	Returns \(f(x)\), the density evaluated at \(x\).
double	barF (double x)
	Returns the complementary distribution function.
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	inverseF (double u)
	Returns the inverse distribution function \(x = F^{-1}(u)\).
double	getMean ()
	Returns the mean.
double	getVariance ()
	Returns the variance.
double	getStandardDeviation ()
	Returns the standard deviation.
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 \([x_a, x_b]\).
Public Member Functions inherited from umontreal.ssj.probdist.Distribution
double	cdf (double x)
	Returns the distribution function \(F(x)\).
double[]	getParams ()
	Returns the parameters of the distribution function in the same order as in the constructors.

Detailed Description

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 \(F\).

Definition at line 43 of file ContinuousDistribution.java.

Member Function Documentation

◆ barF()

double umontreal.ssj.probdist.ContinuousDistribution.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

Implements umontreal.ssj.probdist.Distribution.

Definition at line 80 of file ContinuousDistribution.java.

◆ density()

abstract double umontreal.ssj.probdist.ContinuousDistribution.density ( double x )

abstract

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

Parameters

x	value at which the density is evaluated

Returns: density function evaluated at x

◆ getMean()

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

Returns the mean.

Returns: the mean

Implements umontreal.ssj.probdist.Distribution.

Definition at line 357 of file ContinuousDistribution.java.

◆ getStandardDeviation()

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

Returns the standard deviation.

Returns: the standard deviation

Implements umontreal.ssj.probdist.Distribution.

Definition at line 375 of file ContinuousDistribution.java.

◆ getVariance()

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

Returns the variance.

Returns: the variance

Implements umontreal.ssj.probdist.Distribution.

Definition at line 366 of file ContinuousDistribution.java.

◆ getXinf()

double umontreal.ssj.probdist.ContinuousDistribution.getXinf ( )

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

Returns: lower limit of support

Definition at line 385 of file ContinuousDistribution.java.

◆ getXsup()

double umontreal.ssj.probdist.ContinuousDistribution.getXsup ( )

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

Returns: upper limit of support

Definition at line 395 of file ContinuousDistribution.java.

◆ inverseBisection()

double umontreal.ssj.probdist.ContinuousDistribution.inverseBisection ( double u )

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

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 \([0,1]\)

Definition at line 261 of file ContinuousDistribution.java.

◆ inverseBrent()

double umontreal.ssj.probdist.ContinuousDistribution.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 \(F(a) \le u \le F(b)\), where \(u=F(x)\). The calculations are done with an approximate precision of tol. Returns \(x = F^{-1}(u)\). Restrictions: \(u \in[0,1]\).

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

Definition at line 126 of file ContinuousDistribution.java.

◆ inverseF()

double umontreal.ssj.probdist.ContinuousDistribution.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 \([0,1]\)

Implements umontreal.ssj.probdist.Distribution.

Definition at line 346 of file ContinuousDistribution.java.

◆ setXinf()

void umontreal.ssj.probdist.ContinuousDistribution.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

Definition at line 405 of file ContinuousDistribution.java.

◆ setXsup()

void umontreal.ssj.probdist.ContinuousDistribution.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

Definition at line 415 of file ContinuousDistribution.java.

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

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

SSJ API Documentation Stochastic Simulation in Java

Public Member Functions

Detailed Description

Member Function Documentation

◆ barF()

◆ density()

◆ getMean()

◆ getStandardDeviation()

◆ getVariance()

◆ getXinf()

◆ getXsup()

◆ inverseBisection()

◆ inverseBrent()

◆ inverseF()

◆ setXinf()

◆ setXsup()