fMultivar (version 4031.84)

bvdist-norm2d: Bivariate Normal Distribution

Description

Density, distribution function, and random generation for the bivariate normal distribution.

Usage

dnorm2d(x, y, rho = 0)
pnorm2d(x, y, rho = 0)
rnorm2d(n, rho = 0)

Value

pnorm2d

returns a two column matrix of probabilities for the bivariate normal distribution function.

dnorm2d

returns a two column matrix of densities for the bivariate normal distribution function.

rnorm2d

returns a two column matrix of random deviates generated from the bivariate normal distribution function.

Arguments

x, y

two numeric vectors defining the x and y coordinates.

n

the number of random deviates to be generated, an integer value.

rho

the correlation parameter, a numeric value ranging between minus one and one, by default zero.

Author

Adelchi Azzalini for the underlying pnorm2d function,
Diethelm Wuertz for the Rmetrics R-port.

References

Azzalini A., (2004); The sn Package; R Reference Guide available from www.r-project.org.

Venables W.N., Ripley B.D., (2002); Modern Applied Statistics with S, Fourth Edition, Springer.

Examples

## dnorm2d -
   # Bivariate Normal Density:
   x <- (-40:40)/10
   X <- grid2d(x)
   z <- dnorm2d(X$x, X$y, rho = 0.5)
   ZD <- list(x = x, y = x, z = matrix(z, ncol = length(x)))
   # Perspective Density Plot:
   persp(ZD, theta = -40, phi = 30, col = "steelblue")
   # Contour Density Plot:
   contour(ZD, main="Bivariate Normal Density")
    
## pnorm2d -
   # Bivariate Normal Probability:
   z <- pnorm2d(X$x, X$y, rho = 0.5)
   ZP <- list(x = x, y = x, z = matrix(z, ncol = length(x)))
   # Perspective Plot:
   persp(ZP, theta = -40, phi = 30, col = "steelblue")
   # Contour Plot:
   contour(ZP)
   
## rnorm2d - 
   # Bivariate Normal Random Deviates
   r <- rnorm2d(5000, rho=0.5)
   # Scatter Plot:
   plot(r, col="steelblue", pch=19, cex=0.5) 
   contour(ZD, add=TRUE, lwd=2, col="red")
   # Hexagonal Binning:
   plot(hexBinning(r))
   contour(ZD, add=TRUE, lwd=2, col="black")