R help - Jul 2008 - help about random generation of a Normal distribution of several variables

Hello.

Somebody knows how can I generate a set of n random vectors  of a  
normal distribution of several variables?
For example, I want to generate n=100 random vectors of two dimensions  
for a normal with mean c(0,1)  and  variance matrix:   
matrix(c(2,1,1,3),2,2).

Thanks in advance,

Arnau.

Hello.

Somebody knows how can I generate a set of n random vectors  of a normal
distribution of several variables?
For example, I want to generate n=100 random vectors of two dimensions for
a normal with mean c(0,1)  and  variance matrix:  matrix(c(2,1,1,3),2,2).

Thanks in advance,

Arnau.

Hi, Arnau,

  mvrnorm() in MASS library is what you need.
  ? mvrnorm to see the detail but first you need to load the MASS  
library, i.e,library(MASS)
  regards/
On 2008-7-6, at ??12:21, Arnau Mir wrote:
> Hello.
>
> Somebody knows how can I generate a set of n random vectors  of a  
> normal
> distribution of several variables?
> For example, I want to generate n=100 random vectors of two  
> dimensions for
> a normal with mean c(0,1)  and  variance matrix:  matrix(c(2,1,1,3), 
> 2,2).
>
> Thanks in advance,
>
> Arnau.
>
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
-----------------------------------------------
Peng Jiang ?? ,Ph.D. Candidate
Antai College of Economics & Management
????????
Department of Mathematics
???
Shanghai Jiaotong University (Minhang Campus)
800 Dongchuan Road
200240 Shanghai
P. R. China

On Sat, 2008-07-05 at 18:21 +0200, Arnau Mir wrote:
> Hello.
> 
> Somebody knows how can I generate a set of n random vectors  of a normal
> distribution of several variables?
> For example, I want to generate n=100 random vectors of two dimensions for
> a normal with mean c(0,1)  and  variance matrix:  matrix(c(2,1,1,3),2,2).
One is mvrnorm() in the MASS package, part of the VR bundle that comes
with R.
> require(MASS)
> mu <- c(0,1)
> Sigma <- matrix(c(2,1,1,3),2,2)
> res <- mvrnorm(100, mu = mu, Sigma = Sigma)
> head(res)
           [,1]        [,2]
[1,]  2.7582876  1.04208798
[2,]  0.6364184 -0.08043244
[3,] -1.8897731  0.04051395
[4,]  2.6699881  0.83163661
[5,] -1.1942385 -1.17503716
[6,] -0.4303459 -0.80880649

HTH

G

Hi , Arnau

Did you ever check your mailbox?  your question was answered last  
night  Beijing time. :)
Just read the following .
-------------------------

There is no need to load the MASS library, since the code for
mvrnorm therein is compact and self-contained:

mvrnorm <- function (n=1, mu, Sigma, tol=1e-06, empirical=FALSE)
{
  p <- length(mu)
  if(!all(dim(Sigma) == c(p, p)))
    stop("incompatible arguments")
  eS <- eigen(Sigma, symmetric = TRUE, EISPACK = TRUE)
  ev <- eS$values
  if(!all(ev >= -tol * abs(ev[1])))
    stop("'Sigma' is not positive definite")
  X <- matrix(rnorm(p * n), n)
  if(empirical) {
    X <- scale(X, TRUE, FALSE)
    X <- X %*% svd(X, nu = 0)$v
    X <- scale(X, FALSE, TRUE)
  }
  X <- drop(mu) +
       eS$vectors %*% diag(sqrt(pmax(ev, 0)), p) %*% t(X)
  nm <- names(mu)
  if(is.null(nm) && !is.null(dn <- dimnames(Sigma)))
    nm <- dn[[1]]
  dimnames(X) <- list(nm, NULL)
  if(n == 1)
    drop(X)
  else t(X)
}


Define that function as above, then proceed along the lines suggested
by Gavin Simpson below.

Ted.


On 05-Jul-08 16:43:46, Gavin Simpson wrote:
> On Sat, 2008-07-05 at 18:21 +0200, Arnau Mir wrote:
>> Hello.
>>
>> Somebody knows how can I generate a set of n random vectors of a
>> normal distribution of several variables?
>> For example, I want to generate n=100 random vectors of two
>> dimensions for a normal with mean c(0,1) and variance matrix:
>> matrix(c(2,1,1,3),2,2).
>
> One is mvrnorm() in the MASS package, part of the VR bundle that comes
> with R.
>
>> require(MASS)
>> mu <- c(0,1)
>> Sigma <- matrix(c(2,1,1,3),2,2)
>> res <- mvrnorm(100, mu = mu, Sigma = Sigma)
>> head(res)
>           [,1]        [,2]
> [1,]  2.7582876  1.04208798
> [2,]  0.6364184 -0.08043244
> [3,] -1.8897731  0.04051395
> [4,]  2.6699881  0.83163661
> [5,] -1.1942385 -1.17503716
> [6,] -0.4303459 -0.80880649
>
> HTH
>
> G
--------------------------------------------------------------------
E-Mail: (Ted Harding) <Ted.Harding@manchester.ac.uk>
Fax-to-email: +44 (0)870 094 0861
Date: 05-Jul-08                                       Time: 18:09:23
------------------------------ XFMail ------------------------------

______________________________________________
R-help@r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
On 2008-7-6, at 上午12:13, Arnau Mir Torres wrote:
> Hello.
>
> Somebody knows how can I generate a set of n random vectors  of a  
> normal distribution of several variables?
> For example, I want to generate n=100 random vectors of two  
> dimensions for a normal with mean c(0,1)  and  variance matrix:   
> matrix(c(2,1,1,3),2,2).
>
> Thanks in advance,
>
> Arnau.
>
> ______________________________________________
> R-help@r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
  
	[[alternative HTML version deleted]]

> library(MASS)
> set.seed(22134)
> Y <- mvrnorm(100, mu = c(0,1), Sigma = matrix(c(2,1,1,3),2,2))
> colMeans(Y)
[1] 0.06461359 1.08436419
> var(Y)
         [,1]     [,2]
[1,] 1.683963 1.300363
[2,] 1.300363 3.280612
> 

Bill Venables
CSIRO Laboratories
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AUSTRALIA
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http://www.cmis.csiro.au/bill.venables/ 

-----Original Message-----
From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org]
On Behalf Of Arnau Mir Torres
Sent: Sunday, 6 July 2008 2:14 AM
To: r-help at r-project.org
Subject: [R] help about random generation of a Normal distribution
ofseveral variables

Hello.

Somebody knows how can I generate a set of n random vectors  of a  
normal distribution of several variables?
For example, I want to generate n=100 random vectors of two dimensions  
for a normal with mean c(0,1)  and  variance matrix:   
matrix(c(2,1,1,3),2,2).

Thanks in advance,

Arnau.

______________________________________________
R-help at r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.