# multinormal: The Vectorized Multivariate Random Deviates In mc2d: Tools for Two-Dimensional Monte-Carlo Simulations

## Description

This function is the vectorized version of the rmvnorm from the mvtnorm library. It provides a random number generator for the multivariate normal distribution with varying vectors of means and varying covariance matrixes.

## Usage

 ```1 2``` ```rmultinormal(n, mean, sigma, method=c("eigen", "svd", "chol")) dmultinormal(x, mean, sigma, log=FALSE) ```

## Arguments

 `x` Vector or matrix of quantiles. If x is a matrix, each row is taken to be a quantile. `n` Number of observations. If length(n) > 1, the length is taken to be the number required. `mean` Vector or matrix of means. If a matrix, each row is taken to be a quantile. Default is a vector of 0 of convenient length. `sigma` Covariance vector corresponding to the coercion of the covariance matrix into a vector (if unique for all n or x) or array of covariance vectors (if varying according to n or x). default is a diagonal matrix of convenient sizee. `method` Matrix decomposition used to determine the matrix root of sigma, possible methods are eigenvalue decomposition ("eigen", default), singular value decomposition ("svd"), and Cholesky decomposition ("chol"). `log` Logical; if TRUE, densities d are given as log(d).

## Details

rmvnorm(n, m, s) is equivalent to rmultinormal(n, m, as.vector(s)). dmvnorm(x, m, s) is equivalent to dmultinormal(x, m, as.vector(s)).

If mean and/or sigma is a matrix, the first random deviate will use the first row of mean and/or sigma, the second random deviate will use the second row of mean and/or sigma, ... recycling being permitted by raw. If mean is a vector of length l or is a matrix with l columns, sigma should be a vector of length l x l or a matrix of number of l x 2 columns.

## Note

The use of a varying sigma may be very time consumming.

## 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 39 40 41``` ```## including equivalence with dmvnorm ## mean and sigma as vectors (mean <- c(10, 0)) (sigma <- matrix(c(1, 2, 2, 10), ncol=2)) sigma <- as.vector(sigma) (x <- matrix(c(9, 8, 1, -1), ncol=2)) round(rmultinormal(10, mean, sigma)) dmultinormal(x, mean, sigma) ## Eq dmvnorm(x, mean, matrix(sigma, ncol=2)) ## mean as matrix (mean <- matrix(c(10, 0, 0, 10), ncol=2)) round(rmultinormal(10, mean, sigma)) dmultinormal(x, mean, sigma) ## Eq dmvnorm(x[1, ], mean[1, ], matrix(sigma, ncol=2)) dmvnorm(x[2, ], mean[2, ], matrix(sigma, ncol=2)) ## sigma as matrix (mean <- c(10, 0)) (sigma <- matrix(c(1, 2, 2, 10, 10, 2, 2, 1), nrow=2, byrow=TRUE)) round(rmultinormal(10, mean, sigma)) dmultinormal(x, mean, sigma) ## Eq dmvnorm(x[1, ], mean, matrix(sigma[1, ], ncol=2)) dmvnorm(x[2, ], mean, matrix(sigma[2, ], ncol=2)) ## mean and sigma as matrix (mean <- matrix(c(10, 0, 0, 10), ncol=2)) (sigma <- matrix(c(1, 2, 2, 10, 10, 2, 2, 1), nrow=2, byrow=TRUE)) round(rmultinormal(10, mean, sigma)) dmultinormal(x, mean, sigma) ## Eq dmvnorm(x[1, ], mean[1, ], matrix(sigma[1, ], ncol=2)) dmvnorm(x[2, ], mean[2, ], matrix(sigma[2, ], ncol=2)) (mean <- c(10, 0)) (sigma <- matrix(c(1, 2, 2, 10, 10, 2, 2, 1), nrow=2, byrow=TRUE)) x <- rmultinormal(1000, mean, sigma) plot(x) ```

mc2d documentation built on July 5, 2021, 5:09 p.m.