R: The Vectorized Multivariate Random Deviates

multinormal {mc2d} | R Documentation

## 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 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

    ## 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)

[Package mc2d version 0.1-18 Index]