Re: [R] About truncated distribution
I resend this to expect more responses. Thanks!
Inspired by the responses, I tried to do this analytically.
The idea is that truncated mean and standard deviation could be expressed as
integral forms. So if given truncated mean, sd and truncated point (mut, sdt,
thre), an optim( ) function could be writen to get the parameters. But the
problem is, pdf is needed in advance to shape the normal curve. So I think it
is possible to do this in an iterative optimization, given assummed initial
sigma and mu, if the optimization meets requirements, then the sigma and mu
could be considered as the real numbers.
I tried to do these by :
f - function(x,sigma,mu) (1/(sigma*sqrt(2*pi)))*exp(-(x-mu)^2/(2*sigma^2))
pdf.fun - function(x) x*f(x);
sd.fun - function(x) x^2*f(x); #-- define a few functions
solve.fun - function(sigma,mu,thre,mut,sdt)
{
(mut-integrate(pdf.fun,thre,upper=Inf)$value/integrate(f,thre,upper=Inf)$value)^2
+(sdt -
integrate(sd.fun,thre,upper=Inf)$value/integrate(f,thre,upper=Inf)$value-(integrate(pdf.fun,thre,upper=Inf)$value/integrate(f,thre,upper=Inf)$value)^2)^2
}
I wish this solve.fun ( ) could be minimized and then gives minimum = 5
for( i in 1:100)
{
mu - 200;sigma - 20;
thre - 160;
mut - 230; sdt - 15;
sol.tem - optimize(solve.fun, lower =0.1,upper =100,tol=0.001);
if (sol.tem$minimum = 5) return(sol.tem)
}
I know my codes is just awkward, and not really working. But I expect some
advice and suggestion about the methods. Am I going in a wrong way since I have
been working on it for a long time. Thanks a lot!
Jen
-Original Message-
From:Ritwik Sinha , [EMAIL PROTECTED]
Sent: 2006-09-12, 17:20:04
To:
CC:jennystadt; r-help@stat.math.ethz.ch
Subject: Re: [R] About truncated distribution
However, if you know the point(s) of truncation then you should be able to work
your way back. Look for the mean and variance of a truncated normal, it will
involve mu, sigma and c (point of truncation). You will need to solve for mu
and sigma from two equation. For example look at the wikipedia page on normal
distribution, it has the mean of a truncated normal distribution. Many standard
statistics books should have the rest of the information.
On 9/12/06, Berton Gunter [EMAIL PROTECTED] wrote:
But my question is a bit different. What I know is the mean
and sd after truncation. If I assume the distribution is
normal, how I am gonna develope the original distribution
using this two parameters?
You can't, as they are plainly not sufficient (you need to know the amount
of truncation also). If you have only the mean and sd and neither the actual
data nor the truncation point you're through.
-- Bert Gunter
Genentech
Could anybody give me some advice?
Thanks in advance!
Jen
[[alternative HTML version deleted]]
__
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
and provide commented, minimal, self-contained, reproducible code.
__
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
and provide commented, minimal, self-contained, reproducible code.
--
Ritwik Sinha
Graduate Student
Epidemiology and Biostatistics
Case Western Reserve University
http://darwin.cwru.edu/~rsinha
[[alternative HTML version deleted]]
__
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
and provide commented, minimal, self-contained, reproducible code.
[[alternative HTML version deleted]]
__
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
and provide commented, minimal, self-contained, reproducible code.
Re: [R] About truncated distribution
Inspired by the responses, I tried to do this analytically.
The idea is that truncated mean and standard deviation could be expressed as
integral forms. So if given truncated mean, sd and truncated point (mut, sdt,
thre), an optim( ) function could be writen to get the parameters. But the
problem is, pdf is needed in advance to shape the normal curve. So I think it
is possible to do this in an iterative optimization, given assummed initial
sigma and mu, if the optimization meets requirements, then the sigma and mu
could be considered as the real numbers.
I tried to do these by :
f - function(x,sigma,mu) (1/(sigma*sqrt(2*pi)))*exp(-(x-mu)^2/(2*sigma^2))
pdf.fun - function(x) x*f(x);
sd.fun - function(x) x^2*f(x); #-- define a few functions
solve.fun - function(sigma,mu,thre,mut,sdt)
{
(mut-integrate(pdf.fun,thre,upper=Inf)$value/integrate(f,thre,upper=Inf)$value)^2
+(sdt -
integrate(sd.fun,thre,upper=Inf)$value/integrate(f,thre,upper=Inf)$value-(integrate(pdf.fun,thre,upper=Inf)$value/integrate(f,thre,upper=Inf)$value)^2)^2
}
I wish this solve.fun ( ) could be minimized and then gives minimum = 5
for( i in 1:100)
{
mu - 200;sigma - 20;
thre - 160;
mut - 230; sdt - 15;
sol.tem - optimize(solve.fun, lower =0.1,upper =100,tol=0.001);
if (sol.tem$minimum= 5) return(sol.tem)
}
I know my codes is just awkward, and not really working. But I expect some
advice and suggestion about the methods. Am I going in a wrong way since I have
been working on it for a long time. Thanks a lot!
Jen
-Original Message-
From:Ritwik Sinha , [EMAIL PROTECTED]
Sent: 2006-09-12, 17:20:04
To:
CC:jennystadt; r-help@stat.math.ethz.ch
Subject: Re: [R] About truncated distribution
However, if you know the point(s) of truncation then you should be able to work
your way back. Look for the mean and variance of a truncated normal, it will
involve mu, sigma and c (point of truncation). You will need to solve for mu
and sigma from two equation. For example look at the wikipedia page on normal
distribution, it has the mean of a truncated normal distribution. Many standard
statistics books should have the rest of the information.
On 9/12/06, Berton Gunter [EMAIL PROTECTED] wrote:
But my question is a bit different. What I know is the mean
and sd after truncation. If I assume the distribution is
normal, how I am gonna develope the original distribution
using this two parameters?
You can't, as they are plainly not sufficient (you need to know the amount
of truncation also). If you have only the mean and sd and neither the actual
data nor the truncation point you're through.
-- Bert Gunter
Genentech
Could anybody give me some advice?
Thanks in advance!
Jen
[[alternative HTML version deleted]]
__
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
and provide commented, minimal, self-contained, reproducible code.
__
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
and provide commented, minimal, self-contained, reproducible code.
--
Ritwik Sinha
Graduate Student
Epidemiology and Biostatistics
Case Western Reserve University
http://darwin.cwru.edu/~rsinha
[[alternative HTML version deleted]]
__
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
and provide commented, minimal, self-contained, reproducible code.
[R] About truncated distribution
Hi All,
I tried RSiteSearch('truncated distribution') , and found a lot of threads on
'fitting truncated normal distribution'. No doubt they are all helpful in
fitting the distribution based on the data of known original mean and sd.
But my question is a bit different. What I know is the mean and sd after
truncation. If I assume the distribution is normal, how I am gonna develope the
original distribution using this two parameters? Could anybody give me some
advice? Thanks in advance!
Jen
[[alternative HTML version deleted]]
__
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
and provide commented, minimal, self-contained, reproducible code.
[R] About truncated distribution
Dear listers,
I tried RSiteSearch('truncated distribution') , and found a lot of threads on
'fitting truncated normal distribution'. No doubt they are all helpful in
fitting the distribution based on the data of known original mean and sd.
But my question is a bit different. What I know is the mean and sd after
truncation. If I assume the distribution is normal, how I am gonna develope the
original distribution using this two parameters? Could anybody give me some
advice? Thanks in advance!
Jen
[[alternative HTML version deleted]]
__
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
and provide commented, minimal, self-contained, reproducible code.
Re: [R] About truncated distribution
But my question is a bit different. What I know is the mean and sd after truncation. If I assume the distribution is normal, how I am gonna develope the original distribution using this two parameters? You can't, as they are plainly not sufficient (you need to know the amount of truncation also). If you have only the mean and sd and neither the actual data nor the truncation point you're through. -- Bert Gunter Genentech Could anybody give me some advice? Thanks in advance! Jen [[alternative HTML version deleted]] __ 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 and provide commented, minimal, self-contained, reproducible code. __ 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 and provide commented, minimal, self-contained, reproducible code.
Re: [R] About truncated distribution
However, if you know the point(s) of truncation then you should be able to work your way back. Look for the mean and variance of a truncated normal, it will involve mu, sigma and c (point of truncation). You will need to solve for mu and sigma from two equation. For example look at the wikipedia page on normal distribution, it has the mean of a truncated normal distribution. Many standard statistics books should have the rest of the information. On 9/12/06, Berton Gunter [EMAIL PROTECTED] wrote: But my question is a bit different. What I know is the mean and sd after truncation. If I assume the distribution is normal, how I am gonna develope the original distribution using this two parameters? You can't, as they are plainly not sufficient (you need to know the amount of truncation also). If you have only the mean and sd and neither the actual data nor the truncation point you're through. -- Bert Gunter Genentech Could anybody give me some advice? Thanks in advance! Jen [[alternative HTML version deleted]] __ 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 and provide commented, minimal, self-contained, reproducible code. __ 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 and provide commented, minimal, self-contained, reproducible code. -- Ritwik Sinha Graduate Student Epidemiology and Biostatistics Case Western Reserve University http://darwin.cwru.edu/~rsinha [[alternative HTML version deleted]] __ 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 and provide commented, minimal, self-contained, reproducible code.
