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Re: st: Random draws from multivariate normal not centered at the mean
From
Mauro Caselli <[email protected]>
To
[email protected]
Subject
Re: st: Random draws from multivariate normal not centered at the mean
Date
Tue, 15 Feb 2011 14:51:33 +1100
Hi Fernando,
Thanks a lot for your reply. This looks like the right way to go. I
have to understand better how to implement the inverse mills ratio,
but I see that I need to look at truncated normal distributions.
Thanks again,
Mauro
On 15 February 2011 14:24, Fernando Rios Avila <[email protected]> wrote:
> Hi Mauro,
> I think I understand what exactly you want to do. The only way i can think of that you can be sure that the new draw is not "centered" around the mean is to "correct" the draw using the inverse mills ratio.
> For instance, assume x follows N(u,sigma) and u want to get random draws that will have a mean= u+sigma*normalden((a-u)/sigma)/[1-normal((a-u)/sigma)], where A is just an arbitrary limit,
> you would just need to first btain the random draws xi, and then "correct" them accordingly depending to which mean u want.
> For more references to this, look at references respect to moments for truncated normal distributions.
>
> Once you have the random draws, the draws for the second section of the multivariate normal distribution can simply be generated using the rnormal(), function, where the mean and variance correspond to the conditional normal distribution.
>
> Hope this is what u were looking for.
> Fernando
>>>> David Muller <[email protected]> 02/14/11 8:10 PM >>>
> Hi Mauro,
>
> I'm afraid I don't understand what you're after, and I don't know what
> you are refer to when you use the term 'centered' if you are not
> referring to the mean.
>
> David
>
> On Tue, Feb 15, 2011 at 11:45 AM, Mauro Caselli <[email protected]> wrote:
>> Unfortunately, that doesn't quite do the job. The means() option tells
>> the means of the distribution you draw from, which in my previous
>> example were 4 and 5. But is it possible to draw from that
>> distribution with mean 4 and 5 a set of numbers that are not centered
>> around those means? If you input in the means() option the means that
>> you would like, the draws are from a different distribution and not
>> from the original one I am interested in.
>> I hope that this clears what I am trying to do.
>>
>> Mauro
>>
>>
>>
>> On 15 February 2011 11:10, David Muller <[email protected]> wrote:
>>>
>>> The -means()- option in -drawnorm- does what you require. It's
>>> documented in -help drawnorm-.
>>>
>>> Cheers,
>>> David
>>>
>>> On Tue, Feb 15, 2011 at 10:34 AM, Mauro Caselli <[email protected]> wrote:
>>> > Dear Stata users,
>>> >
>>> > I have the following question:
>>> > I have a multivariate normal distribution with two variables
>>> > (therefore I have means and variances of both and the correlation
>>> > coefficient). I want to draw psuedo-random draws from this
>>> > distribution and I know that this can be done with the command
>>> > drawnorm. However, I would like to have draws not centered at the mean
>>> > of the population but rather at a different value of one of the two
>>> > variables.
>>> > So, if the means are 4 for x and 5 for y, for instance I would like to
>>> > draw ten numbers that give an average of 3 for x and follow the
>>> > multivariate normal to give the relative values of y. Is this possible
>>> > with drawnorm? If not, can anyone point me in the right direction?
>>> >
>>> > Thank you very much.
>>> >
>>> > With best wishes,
>>> >
>>> > Mauro
>>> >
>>> >
>>> >
>>> > --
>>> > Mauro Caselli
>>> > Postdoctoral Research Fellow
>>> > School of Economics, Room 410
>>> > Australian School of Business
>>> > The University of New South Wales, NSW, 2052
>>> > Australia
>>> > Phone: +61 (0)2 9385 3561
>>> > Email: [email protected]
>>> > *
>>> > * For searches and help try:
>>> > * http://www.stata.com/help.cgi?search
>>> > * http://www.stata.com/support/statalist/faq
>>> > * http://www.ats.ucla.edu/stat/stata/
>>> >
>>>
>>> *
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>>
>>
>>
>> --
>> Mauro Caselli
>> Postdoctoral Research Fellow
>> School of Economics, Room 410
>> Australian School of Business
>> The University of New South Wales, NSW, 2052
>> Australia
>> Phone: +61 (0)2 9385 3561
>> Email: [email protected]
>>
>> *
>> * For searches and help try:
>> * http://www.stata.com/help.cgi?search
>> * http://www.stata.com/support/statalist/faq
>> * http://www.ats.ucla.edu/stat/stata/
>>
>
> *
> * For searches and help try:
> * http://www.stata.com/help.cgi?search
> * http://www.stata.com/support/statalist/faq
> * http://www.ats.ucla.edu/stat/stata/
>
>
> *
> * For searches and help try:
> * http://www.stata.com/help.cgi?search
> * http://www.stata.com/support/statalist/faq
> * http://www.ats.ucla.edu/stat/stata/
>
--
Mauro Caselli
Postdoctoral Research Fellow
School of Economics, Room 410
Australian School of Business
The University of New South Wales, NSW, 2052
Australia
Phone: +61 (0)2 9385 3561
Email: [email protected]
*
* For searches and help try:
* http://www.stata.com/help.cgi?search
* http://www.stata.com/support/statalist/faq
* http://www.ats.ucla.edu/stat/stata/