Classes implementing 2-dimensional continuous distributions should inherit from this class. More...
Public Member Functions | |
| abstract double | density (double x, double y) |
| Returns \(f(x, y)\), the density of \((X, Y)\) evaluated at \((x, y)\). | |
| double | density (double[] x) |
| Simply calls density (x[0], x[1]). | |
| abstract double | cdf (double x, double y) |
| Computes the distribution function \(F(x, y)\): | |
| double | barF (double x, double y) |
| Computes the upper cumulative distribution function. | |
| double | cdf (double a1, double a2, double b1, double b2) |
| Computes the cumulative probability in the square region. | |
| Public Member Functions inherited from umontreal.ssj.probdistmulti.ContinuousDistributionMulti | |
| 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. | |
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. | |
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.
Definition at line 44 of file ContinuousDistribution2Dim.java.
Member Function Documentation
◆ barF()
| double umontreal.ssj.probdistmulti.ContinuousDistribution2Dim.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 \((x, y)\)
Reimplemented in umontreal.ssj.probdistmulti.BiNormalDist, umontreal.ssj.probdistmulti.BiNormalDonnellyDist, umontreal.ssj.probdistmulti.BiNormalGenzDist, and umontreal.ssj.probdistmulti.BiStudentDist.
Definition at line 106 of file ContinuousDistribution2Dim.java.
◆ cdf() [1/2]
| double umontreal.ssj.probdistmulti.ContinuousDistribution2Dim.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
Definition at line 126 of file ContinuousDistribution2Dim.java.
◆ cdf() [2/2]
|
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 \((x, y)\)
Reimplemented in umontreal.ssj.probdistmulti.BiNormalDist, umontreal.ssj.probdistmulti.BiNormalDonnellyDist, umontreal.ssj.probdistmulti.BiNormalGenzDist, and umontreal.ssj.probdistmulti.BiStudentDist.
◆ density() [1/2]
|
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 \((x, y)\)
Reimplemented in umontreal.ssj.probdistmulti.BiNormalDist, and umontreal.ssj.probdistmulti.BiStudentDist.
◆ density() [2/2]
| double umontreal.ssj.probdistmulti.ContinuousDistribution2Dim.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 \((x[0], x[1])\)
Reimplemented from umontreal.ssj.probdistmulti.ContinuousDistributionMulti.
Definition at line 80 of file ContinuousDistribution2Dim.java.
Member Data Documentation
◆ decPrec
| int umontreal.ssj.probdistmulti.ContinuousDistribution2Dim.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.
Definition at line 51 of file ContinuousDistribution2Dim.java.
The documentation for this class was generated from the following file:
- src/main/java/umontreal/ssj/probdistmulti/ContinuousDistribution2Dim.java
