Re: [R] generate bi-variate normal data

From: Liaw, Andy <andy_liaw_at_merck.com>
Date: Thu 06 Jul 2006 - 03:53:12 EST


If (X, Y) ~ N(mx, my, sx^2, sy^2, r) (r being the correlation, not covariance), then

Y|X ~ N(my + r * (sy / sx) * (X - mx), sy^2 * (1 - r^2))

You can use this to work out what you need to do.

Best,
Andy


	From: Shin, David [mailto:david.shin@pearson.com] 
	Sent: Wednesday, July 05, 2006 1:14 PM
	To: Liaw, Andy; 'r-help@stat.math.ethz.ch'
	Subject: RE: [R] generate bi-variate normal data [Broadcast]
	
	

	Thanks for Andy's comment and help. I should have used a better
example for my question. Below is my exact question and I will appreciate a lot for any insights.

        I generate a bi-variate normal distribution with mean = c(0, 0.2) and variance covariance matrix = matrix(c(1, .025, .025, .0025), nrow = 2):

> x <- rmvnorm(10, c(0, 0.2), matrix(c(1, .025, .025, .0025), nrow =
2))

> x

                    [,1] [,2]

         [1,] 0.1595351 0.1715898

         [2,] -0.5177577 0.1839222

         [3,] -0.8794011 0.1896593

         [4,] 1.0584185 0.2208470

         [5,] 0.1960055 0.2199169

         [6,] 0.6450406 0.1773001

         [7,] -2.2160986 0.1810803

         [8,] 0.2131569 0.1223121

         [9,] -0.3598349 0.2402232

        [10,] -0.3905455 0.1787059

> x.sum <- apply(x,1,sum)

> x.sum

         [1] 0.3311249 -0.3338355 -0.6897418 1.2792655 0.4159225 0.8223407 -2.0350183 0.3354690 -0.1196116 -0.2118395

        if I call x[,1] as theta.year1 and x[,2] as growth.year1 then the mean of x.sum is 0+0.2 = -.2 and the standard deviation of x.sum is sqrt(1+.0025+2*.5*1*.05) = 1.0259

        <<...OLE_Obj...>>

        assume the correlation is again 0.5, I would like to generate another bi-variate normal distribution with the fixed first column that equals to x.sum. If the mean and SD of the second column is 0.2 and 0.05, respectively, the mean of this bi-variate normal distribution is c(0.2, 0.2) and the variance-covariance matrix is: matrix(c(1.0259^2, 0.5*1.0259*0.05, 0.5*1.0259*0.05, 0.0025), 2)

        Thanks again for helping me.

        David

		-----Original Message-----
	From: Liaw, Andy [mailto:andy_liaw@merck.com]
	Sent: Wednesday, July 05, 2006 11:50 AM
	To: Shin, David; 'r-help@stat.math.ethz.ch'
	Subject: RE: [R] generate bi-variate normal data

	From: Shin, David


>

> 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)
x.sum as you described would be distributed as normal with mean=0
and

        variance=2 (so you might as well just use x.sum <- rnorm(10, 0, sqrt(2))),

        so I don't see how you can get to the second step where you want x.sum to

        have variance=1. Also, since the covariances are 0, you could just generate

        the columns separately using rnorm() and cbind() them together.

        It might be helpful for you to get some basic understanding of math stat. I

        only say that because most likely there are other steps to whatever task you

        are doing (people are unlikely to be generating random numbers just for

        kicks), and there's no telling what other things you are doing

        inefficiently, or even erroneously.

        Andy          

> I will appreciate for all insights.

>

> David s.

>

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