ContinuousDistribution Class Reference

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

Inheritance diagram for ContinuousDistribution:

Collaboration diagram for ContinuousDistribution:

Public Member Functions
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...
Public Member Functions inherited from Distribution
double	cdf (double x)
	Returns the distribution function \(F(x)\). More...
double []	getParams ()
	Returns the parameters of the distribution function in the same order as in the constructors.

Public Attributes
int	decPrec = 15

Protected Attributes
double	supportA = Double.NEGATIVE_INFINITY
double	supportB = Double.POSITIVE_INFINITY

Static Protected Attributes
static final double	XBIG = 100.0
static final double	XBIGM = 1000.0
static final double []	EPSARRAY

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 \(F\).

Member Function Documentation

barF()

double 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 Distribution.

density()

abstract double 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 getMean

(

)

Returns the mean.

Returns

the mean

Implements Distribution.

getStandardDeviation()

double getStandardDeviation

(

)

Returns the standard deviation.

Returns

the standard deviation

Implements Distribution.

getVariance()

double getVariance

(

)

Returns the variance.

Returns

the variance

Implements Distribution.

getXinf()

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()

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

inverseBisection()

double 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 \([0,1]\)

inverseBrent()

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 \(F(a) \le u \le F(b)\), 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

inverseF()

double 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 Distribution.

setXinf()

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()

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

Member Data Documentation

EPSARRAY

final double [] EPSARRAY

staticprotected

Initial value:

= {
    0.5, 0.5E-1, 0.5E-2, 0.5E-3, 0.5E-4, 0.5E-5, 0.5E-6, 0.5E-7, 0.5E-8,
    0.5E-9, 0.5E-10, 0.5E-11, 0.5E-12, 0.5E-13, 0.5E-14, 0.5E-15, 0.5E-16,
    0.5E-17, 0.5E-18, 0.5E-19, 0.5E-20, 0.5E-21, 0.5E-22, 0.5E-23, 0.5E-24,
    0.5E-25, 0.5E-26, 0.5E-27, 0.5E-28, 0.5E-29, 0.5E-30, 0.5E-31, 0.5E-32,
    0.5E-33, 0.5E-34, 0.5E-35
    }

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

• ContinuousDistribution.java