# zzz-mvnorm: Multivariate Normal Distribution In fMultivar: Rmetrics - Analysing and Modeling Multivariate Financial Return Distributions

## Description

Alternative density, distribution function, and random generation for the multivariate Normal distribution.

## Details

The multivariate distribution functions to compute densities `dmvnorm`, probabilities `pmvnorm`, and to generate random numbers `rmvnorm` are available from the contributed R package `mvtnorm`. The function `qmvnorm` computes the equicoordinate quantile function of the multivariate normal distribution for arbitrary correlation matrices based on inversion of `pmvnorm`.

`dmvnorm(x, mean, sigma, <<...>>`
`pmvnorm(<<...>>)`
`qmvnorm(p, <<...>>)`
`rmvnorm(n, mean, sigma, <<...>>`

NOTE: The function are not builtin in the package `fMultivar`. Fur details we refer to the help page of `mvnorm`.

## Author(s)

Friedrich Leisch and Fabian Scheipl.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38``` ```## Not run: ## Load Libray: require(mvtnorm) ## dmvnorm - # Multivariate Normal Density Function: mean <- c(1, 1) sigma <- matrix(c(1, 0.5, 0.5, 1), ncol=2) dmvnorm(x = c(0, 0),mean, sigma) ## dmvnorm - # Across a Grid: x <- seq(-4, 4, length=90) X <- grid2d(x) X <- cbind(X\$x, X\$y) # Write Density Function: dmvnorm. <- function(X, mean, sigma) matrix(apply(X, 1, dmvnorm, mean=mean, sigma=sigma), ncol=sqrt(dim(X)[1])) z <- dmvnorm.(X, mean, sigma) contour(list(x = x, y = x, z = z)) ## qmvnorm - # Equicoordinate Quantile Function: qmvnorm(p = 0.95, sigma = diag(2), tail = "both") ## rmvnorm - # Random Numbers: sigma <- matrix(c(4, 2, 2, 3), ncol=2) x <- rmvnorm(n = 500, mean = c(1, 2), sigma = sigma) colMeans(x) var(x) # Next Generation: x <- rmvnorm(n = 500, mean = c(1, 2), sigma = sigma, method = "chol") colMeans(x) var(x) plot(x, cex=0.5, pch=19, col="steelblue") ## End(Not run) ```

fMultivar documentation built on Nov. 17, 2017, 2:19 p.m.