umontreal.iro.lecuyer.probdistmulti

Class ContinuousDistribution2Dim

java.lang.Object

umontreal.iro.lecuyer.probdistmulti.ContinuousDistributionMulti

umontreal.iro.lecuyer.probdistmulti.ContinuousDistribution2Dim

Direct Known Subclasses:

BiNormalDist, BiStudentDist

public abstract class ContinuousDistribution2Dim
extends ContinuousDistributionMulti

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 bar(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.

Field Summary

Fields

Modifier and Type	Field and Description
int	decPrec Defines the target number of decimals of accuracy when approximating a distribution function, but there is no guarantee that this target is always attained.

Constructor Summary

Constructors

Constructor and Description
ContinuousDistribution2Dim()

Method Summary

Methods

Modifier and Type	Method and Description
double	barF(double x, double y) .
abstract double	cdf(double x, double y) .
double	cdf(double a1, double a2, double b1, double b2) .
double	density(double[] x) Simply calls density (x[0], x[1]).
abstract double	density(double x, double y) Returns f (x, y), the density of (X, Y) evaluated at (x, y).

Methods inherited from class umontreal.iro.lecuyer.probdistmulti.ContinuousDistributionMulti

getCorrelation, getCovariance, getDimension, getMean

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

decPrec

public int decPrec

Defines the target number of decimals of accuracy when approximating a distribution function, but there is no guarantee that this target is always attained.

Constructor Detail

ContinuousDistribution2Dim

public ContinuousDistribution2Dim()

Method Detail

density

public abstract double density(double x,
             double y)

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

public double density(double[] x)

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

Specified by:

density in class ContinuousDistributionMulti

Parameters:

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

Returns:

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

cdf

public abstract double cdf(double x,
         double y)

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

F(x, y) = P[X <= x, Y <= y] = ∫_-∞^xds∫_-∞^ydt 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)

barF

public double barF(double x,
          double y)

. Computes the upper cumulative distribution function bar(F)(x, y):

bar(F)(x, y) = P[X >= x, Y >= y] = ∫^∞_xds∫^∞_ydt 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

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

. Computes the cumulative probability in the square region

P[a₁ <= X <= b₁, a₂ <= Y <= b₂] = ∫_a1^b₁dx∫_a2^b₂dy 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