SSJ
V. 2.6.

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 ContinuousDistribution2Dimextends 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
` 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
`ContinuousDistribution2Dim()`

Method Summary
` 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] = ∫xdsydt 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 <= b1a2 <= Y <= b2] = ∫a1b1dxa2b2dy 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

SSJ
V. 2.6.

To submit a bug or ask questions, send an e-mail to Pierre L'Ecuyer.