multinormal: The Vectorized Multivariate Random Deviates

In mc2d: Tools for Two-Dimensional Monte-Carlo Simulations

The Vectorized Multivariate Random Deviates

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

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 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.

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)

mc2d documentation built on June 22, 2024, 10:54 a.m.