# Re: [R] generate bi-variate normal data

From: <markleeds_at_verizon.net>
Date: Sat 01 Jul 2006 - 15:27:09 EST

>From: "Shin, David" <david.shin@pearson.com>
>Date: Sat Jul 01 00:15:21 CDT 2006
>To: "'r-help@stat.math.ethz.ch'" <r-help@stat.math.ethz.ch>
>Subject: [R] generate bi-variate normal data

it's an interesting question. someone else on this list can answer more explicitly but i think you have to use the result for the multivariate normal distribution ( bivariate case ) where , if the joint is normal , then the conditional is normal also with parameters a function of the 2 means and the elements of the covariance matrix. the result in any decent mathematical statistics such as casella berger. so, given the one column, generate the other column conditionally using the formula and then the joint dist will be bivariate normal.

>Dear all,
>
>I would like to generate bi-variate normal data given that the first column
>of the data is known. for example:
>I first generate a set of data using the command,
>x <- rmvnorm(10, c(0, 0), matrix(c(1, 0, 0, 1), 2))
>
>then I would like to sum up the two columns of x:
>x.sum <- apply(x, 1, sum)
>
>now with x.sum I would like to generate another column of data, say y, that
>makes cbind(x.sum, y) follow a bi-variate normal distribution with mean =
>c(0, 0) and sigma = matrix(c(1, 0, 0, 1),2)
>
>I will appreciate for all insights.
>
>David s.
>
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