ContinuousDistribution2Dim Class Reference

Classes implementing 2-dimensional continuous distributions should inherit from this class. More...

Inheritance diagram for ContinuousDistribution2Dim:

Collaboration diagram for ContinuousDistribution2Dim:

Public Member Functions
abstract double	density (double x, double y)
	Returns \(f(x, y)\), the density of \((X, Y)\) evaluated at \((x, y)\). More...
double	density (double[] x)
	Simply calls density (x[0], x[1]). More...
abstract double	cdf (double x, double y)
	Computes the distribution function \(F(x, y)\): \[ F(x, y) = P[X\le x, Y \le y] = \int_{-\infty}^x ds \int_{-\infty}^y dt  f(s, t). \] . More...
double	barF (double x, double y)
	Computes the upper cumulative distribution function \(\overline{F}(x, y)\): \[ \overline{F}(x, y) = P[X\ge x, Y \ge y] = \int^{\infty}_x ds \int^{\infty}_y dt  f(s, t). \] . More...
double	cdf (double a1, double a2, double b1, double b2)
	Computes the cumulative probability in the square region \[ P[a_1 \le X \le b_1,\: a_2 \le Y \le b_2] = \int_{a_1}^{b_1} dx \int_{a_2}^{b_2} dy  f(x, y). \] . More...
Public Member Functions inherited from ContinuousDistributionMulti
abstract double	density (double[] x)
	Returns \(f(x_1, x_2, …, x_d)\), the probability density of \(X\) evaluated at the point \(x\), where \(x = \{x_1, x_2, …, x_d\}\). More...
int	getDimension ()
	Returns the dimension \(d\) of the distribution.
abstract double []	getMean ()
	Returns the mean vector of the distribution, defined as \(\mu_i = E[X_i]\).
abstract double [][]	getCovariance ()
	Returns the variance-covariance matrix of the distribution, defined as \(\sigma_{ij} = E[(X_i - \mu_i)(X_j - \mu_j)]\).
abstract double [][]	getCorrelation ()
	Returns the correlation matrix of the distribution, defined as \(\rho_{ij} = \sigma_{ij}/\sqrt{\sigma_{ii}\sigma_{jj}}\).

Public Attributes
int	decPrec = 15
	Defines the target number of decimals of accuracy when approximating a distribution function, but there is no guarantee that this target is always attained.

Static Protected Attributes
static final double	XINF = Double.MAX_VALUE
static final double	XBIG = 1000.0
static final double []	EPSARRAY

Additional Inherited Members
Protected Attributes inherited from ContinuousDistributionMulti
int	dimension

Detailed Description

Classes implementing 2-dimensional continuous distributions should inherit from this class.

Such distributions are characterized by a density function \(f(x, y)\); thus the signature of a density method is supplied here. This class also provides a default implementation of \(\overline{F}(x, y)\), the upper CDF. The inverse function \(F^{-1}(u)\) represents a curve \(y = h(x)\) of constant \(u\) and it is not implemented.

Member Function Documentation

barF()

double barF	(	double	x,
		double	y
	)

Computes the upper cumulative distribution function \(\overline{F}(x, y)\):

\[ \overline{F}(x, y) = P[X\ge x, Y \ge y] = \int^{\infty}_x ds \int^{\infty}_y dt  f(s, t). \]

.

Parameters

x	value \(x\) at which the upper distribution is evaluated
y	value \(y\) at which the upper distribution is evaluated

Returns

upper distribution function evaluated at \((x, y)\)

cdf() [1/2]

abstract double cdf ( double  x, double  y  )

abstract

Computes the distribution function \(F(x, y)\):

\[ F(x, y) = P[X\le x, Y \le y] = \int_{-\infty}^x ds \int_{-\infty}^y dt  f(s, t). \]

.

Parameters

x	value \(x\) at which the distribution function is evaluated
y	value \(y\) at which the distribution function is evaluated

Returns

distribution function evaluated at \((x, y)\)

cdf() [2/2]

double cdf	(	double	a1,
		double	a2,
		double	b1,
		double	b2
	)

Computes the cumulative probability in the square region

\[ P[a_1 \le X \le b_1,\: a_2 \le Y \le b_2] = \int_{a_1}^{b_1} dx \int_{a_2}^{b_2} dy  f(x, y). \]

.

Parameters

a1	\(x\) lower limit of the square
a2	\(y\) lower limit of the square
b1	\(x\) upper limit of the square
b2	\(y\) upper limit of the square

Returns

the cumulative probability in the square region

density() [1/2]

abstract double density ( double  x, double  y  )

abstract

Returns \(f(x, y)\), the density of \((X, Y)\) evaluated at \((x, y)\).

Parameters

x	value \(x\) at which the density is evaluated
y	value \(y\) at which the density is evaluated

Returns

density function evaluated at \((x, y)\)

density() [2/2]

double density

(

double []

x

)

Simply calls density (x[0], x[1]).

Parameters

x	point \((x[0], x[1])\) at which the density is evaluated

Returns

density function evaluated at \((x[0], x[1])\)

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:

• ContinuousDistribution2Dim.java