# dmvnorm: Multivariate Normal (Gaussian) distribution In Rsafd: Statistical Analysis of Financial Data in R

## Description

The mean of the distribution may be a d-dimensional vector. The covariance matrix should be given as a d x d non-negative definite matrix if supplied with the parameter `cov`. It can also be given, if cov is missing, by a vector `sd` for the marginal standard deviations and a scalar `rho` implying a constant correlation between all the marginals. If the covariance structure of the marginals is supplied in this way, `sd` should be a d-dimensional vector, and `rho` should be scalar. The dimension `d` may be inferred from other arguments. The code of this function is a mere wrapper for the function with the same name from the library `mvtnorm`. It was written to provide compatibility with S-Plus, hence the long list of parameters

## Usage

 ```1 2 3 4 5``` ```dmvnorm(x, mean = rep(0, d), cov = diag(d), sd, rho, d = 2, sigma = cov, log = FALSE) pmvnorm(x, mean = rep(0, d), cov = diag(d), sd, rho, d = 2, sigma = cov, log = FALSE) rmvnorm(n, mean = rep(0, d), cov = diag(d), sd, rho, d = 2, sigma = cov, log = FALSE) ```

## Arguments

 `n` Number of samples generated by `rmvnorm` `x` n x d numeric matrix, each row giving a point at which the density is computed `mean` d- dimensional vector giving the mean of the distribution `cov` d x d matrix giving the covariance matrix of the distribution `sd` d- vector of the marginal standard deviations `rho` number giving the constant correlation when the covariance matrix is given by its diagonal and the parameter `rho` `d` dimension of the distribution `sigma` used for compatibility with S-Plus `log` boolean for logarithmic scale `method` String giving the method SVD or Choleski used

## Details

`dmvnorm`,compute multivariate normal density. `pmvnorm` compute multivariate normal c.d.f. `rmvnorm` generate random samples from the multivariate normal distribution.

## Value

A list of the elements

 `\$x` n x d Matrix giving the values where the density is computed `\$y` Vector of length `n` giving the values of the density

Rene Carmona

## References

library `Rmetrics` and `S-Plus` manual

`dnorm`
 ```1 2 3 4 5``` ```## Not run: TSAMPLE <- rmvnorm(n=128, mean=rep(0,2), sd=rep(1,2), rho=.18) TDENS <- kdest(TSAMPLE[,1], TSAMPLE[,2]) ## End(Not run) ```