umontreal.iro.lecuyer.probdist
Class BiNormalDonnellyDist

java.lang.Object
  umontreal.iro.lecuyer.probdist.ContinuousDistribution2Dim
      umontreal.iro.lecuyer.probdist.BiNormalDist
          umontreal.iro.lecuyer.probdist.BiNormalDonnellyDist

public class BiNormalDonnellyDist
extends BiNormalDist

Extends the class BiNormalDist for the bivariate normal distribution using a translation of Donnelly's FORTRAN code.

Field Summary

Fields inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution2Dim

decPrec

Constructor Summary

BiNormalDonnellyDist(double rho)
Constructs a BiNormalDonnellyDist object with default parameters μ₁ = μ₂ = 0, σ₁ = σ₂ = 1 and correlation ρ = rho.

BiNormalDonnellyDist(double mu1, double sigma1, double mu2, double sigma2, double rho)
Constructs a BiNormalDonnellyDist object with parameters μ₁ = mu1, μ₂ = mu2, σ₁ = sigma1, σ₂ = sigma2 and ρ = rho.

Method Summary

double	barF(double x, double y) .
static double	barF(double x, double y, double rho)
static double	barF(double mu1, double sigma1, double x, double mu2, double sigma2, double y, double rho)
double	cdf(double x, double y) .
static double	cdf(double x, double y, double rho) Computes the standard binormal distribution with the method described in.
static double	cdf(double mu1, double sigma1, double x, double mu2, double sigma2, double y, double rho)

Methods inherited from class umontreal.iro.lecuyer.probdist.BiNormalDist

density, density, density, getMu1, getMu2, getSigma1, getSigma2

Methods inherited from class java.lang.Object

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

Constructor Detail

BiNormalDonnellyDist

public BiNormalDonnellyDist(double rho)

Constructs a BiNormalDonnellyDist object with default parameters μ₁ = μ₂ = 0, σ₁ = σ₂ = 1 and correlation ρ = rho.

BiNormalDonnellyDist

public BiNormalDonnellyDist(double mu1,
                            double sigma1,
                            double mu2,
                            double sigma2,
                            double rho)

Constructs a BiNormalDonnellyDist object with parameters μ₁ = mu1, μ₂ = mu2, σ₁ = sigma1, σ₂ = sigma2 and ρ = rho.

Method Detail

cdf

public static double cdf(double x,
                         double y,
                         double rho)

Computes the standard binormal distribution with the method described in. The code was translated from the Fortran program written by T. G. Donnelly and is copyrighted by the ACM (see http://www.acm.org/pubs/copyright_policy/#Notice). The absolute error is expected to be smaller than 10^-15.

cdf

public double cdf(double x,
                  double y)

Description copied from class: ContinuousDistribution2Dim

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

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

Overrides:

cdf in class BiNormalDist

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

public static double cdf(double mu1,
                         double sigma1,
                         double x,
                         double mu2,
                         double sigma2,
                         double y,
                         double rho)

barF

public double barF(double x,
                   double y)

Description copied from class: ContinuousDistribution2Dim

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

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

The default implementation computes bar(F)(x, y) = 1 + F(x, y) - F(∞, y) - F(x,∞).

Overrides:

barF in class BiNormalDist

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)

barF

public static double barF(double mu1,
                          double sigma1,
                          double x,
                          double mu2,
                          double sigma2,
                          double y,
                          double rho)

barF

public static double barF(double x,
                          double y,
                          double rho)