multinormal function

The Vectorized Multivariate Random Deviates

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.

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

Examples

## 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)

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 size.
• 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 consuming.