Re: [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: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED]
Sent: Saturday, July 01, 2006 12:27 AM
To: Shin, David
Cc: r-help@stat.math.ethz.ch
Subject: Re: [R] generate bi-variate normal data
From: Shin, David [EMAIL PROTECTED]
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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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...{{dropped}}
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Re: [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:[EMAIL PROTECTED]
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}}
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Re: [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:[EMAIL PROTECTED]
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:[EMAIL PROTECTED]
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}}
__
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Notice: This e-mail message, together with any attachments,
contains information of Merck Co., Inc. (One Merck Drive, Whitehouse
Station, New Jersey, USA 08889), and/or its affiliates (which may be known
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
[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.
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
Re: [R] generate bi-variate normal data
From: Shin, David [EMAIL PROTECTED]
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.
This email may contain confidential material.\ If you were n...{{dropped}}
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