# bvdist-cauchy2d: Bivariate Cauchy Distribution In fMultivar: Rmetrics - Analysing and Modeling Multivariate Financial Return Distributions

## Description

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

## Usage

 ```1 2 3``` ```dcauchy2d(x, y, rho = 0) pcauchy2d(x, y, rho = 0) rcauchy2d(n, rho = 0) ```

## 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.

## Value

`pcauchy2d`
returns a two column matrix of probabilities for the bivariate Cauchy distribution function.

`dcauchy2d`
returns a two column matrix of densities for the bivariate Cauchy distribution function.

`rcauchy2d`
returns a two column matrix of random deviates generated from the bivariate Cauchy distribution function.

## Author(s)

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

 ``` 1 2 3 4 5 6 7 8 9 10 11 12``` ```## Bivariate Cauchy Density: x <- (-40:40)/10 X <- grid2d(x) z <- dcauchy2d(X\$x, X\$y, rho = 0.5) Z <- list(x = x, y = x, z = matrix(z, ncol = length(x))) ## Perspective Density Plot: persp(Z, theta = -40, phi = 30, col = "steelblue") ## Image Density Plot with Contours: image(Z, main="Bivariate Cauchy") contour(Z, add=TRUE) ```

### Example output  ```Loading required package: timeDate

Rmetrics Package fBasics
Analysing Markets and calculating Basic Statistics
Copyright (C) 2005-2014 Rmetrics Association Zurich
Educational Software for Financial Engineering and Computational Science
Rmetrics is free software and comes with ABSOLUTELY NO WARRANTY.
https://www.rmetrics.org --- Mail to: info@rmetrics.org

Rmetrics Package fMultivar
Analysing and Modeling Multivariate Financial Return Distributions
Copyright (C) 2005-2014 Rmetrics Association Zurich
Educational Software for Financial Engineering and Computational Science
Rmetrics is free software and comes with ABSOLUTELY NO WARRANTY.
https://www.rmetrics.org --- Mail to: info@rmetrics.org
```

fMultivar documentation built on March 13, 2020, 3:06 a.m.