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Shin, David

2006-Jul-01 05:15 UTC

[R] generate bi-variate normal data

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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markleeds at verizon.net

2006-Jul-01 05:27 UTC

head link

[R] generate bi-variate normal data

>From: "Shin, David" <david.shin at pearson.com>
>Date: Sat Jul 01 00:15:21 CDT 2006
>To: "'r-help at stat.math.ethz.ch'" <r-help at
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.
>
>****************************************************************************
>This email may contain confidential material.\ If you were n...{{dropped}}
>
>______________________________________________
>R-help at stat.math.ethz.ch mailing list
>https://stat.ethz.ch/mailman/listinfo/r-help
>PLEASE do read the posting guide!
http://www.R-project.org/posting-guide.html

Shin, David

2006-Jul-05 14:59 UTC

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[R] generate bi-variate normal data

Mark,

Thanks. I am still waiting for someone to help me with this matter. I will
appreciate for any insight from you or the others.

Thanks.

David


-----Original Message-----
From: markleeds at verizon.net [mailto:markleeds at verizon.net] 
Sent: Saturday, July 01, 2006 12:27 AM
To: Shin, David
Cc: r-help at stat.math.ethz.ch
Subject: Re: [R] generate bi-variate normal data
>From: "Shin, David" <david.shin at pearson.com>
>Date: Sat Jul 01 00:15:21 CDT 2006
>To: "'r-help at stat.math.ethz.ch'" <r-help at
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.
>
>***************************************************************************
* >This email may contain confidential material.\ If you were n...{{dropped}}
>
>______________________________________________
>R-help at stat.math.ethz.ch mailing list
>https://stat.ethz.ch/mailman/listinfo/r-help
>PLEASE do read the posting guide!http://www.R-project.org/posting-guide.html

**************************************************************************** 
This email may contain confidential material.\ If you were n...{{dropped}}

Liaw, Andy

2006-Jul-05 16:50 UTC

head link

[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.
> 
> **************************************************************
> **************
> This email may contain confidential material.\ If you were...{{dropped}}

Shin, David

2006-Jul-05 17:14 UTC

head link

[R] generate bi-variate normal data

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.
> 
> **************************************************************
> **************
> This email may contain confidential material.\ If you were 
> n...{{dropped}}
> 
> ______________________________________________
> R-help@stat.math.ethz.ch mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide! 
> http://www.R-project.org/posting-guide.html
> 
> 

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Liaw, Andy

2006-Jul-05 17:53 UTC

head link

[R] generate bi-variate normal data

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 at pearson.com] 
	Sent: Wednesday, July 05, 2006 1:14 PM
	To: Liaw, Andy; 'r-help at 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 at merck.com]
	Sent: Wednesday, July 05, 2006 11:50 AM
	To: Shin, David; 'r-help at 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.

	> 

	> **************************************************************

	> **************

	> This email may contain confidential material.\ If you were 

	> n...{{dropped}}

	> 

	> ______________________________________________

	> R-help at stat.math.ethz.ch mailing list

	> https://stat.ethz.ch/mailman/listinfo/r-help

	> PLEASE do read the posting guide! 

	> http://www.R-project.org/posting-guide.html

	> 

	> 


	
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	Notice:  This e-mail message, together with any attachments,
contains information of Merck & Co., Inc. (One Merck Drive, Whitehouse
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outside the United States as Merck Frosst, Merck Sharp & Dohme or MSD and in
Japan, as Banyu) that may be confidential, proprietary copyrighted and/or
legally privileged. It is intended solely for the use of the individual or
entity named on this message.  If you are not the intended recipient, and
have received this message in error, please notify us immediately by reply
e-mail and then delete it from your system.

	
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