# 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.