# [R] Help finding the proper function

Rolf Turner r.turner at auckland.ac.nz
Thu Oct 23 02:34:03 CEST 2008

```Your terminology is confused.  At least it confuses me. I think you are
mixing up ``bivariate distributions'' and ``mixture'' (of two)
distributions.

What you get by rbinding x.1 and x.2 is a sample from a mixture of
two *bivariate*
(Gaussian) distributions, one with mean c(0,0), and one with mean c
(3,4).

Of course x.3 is a sample from a single *bivariate* Gaussian
distribution with
mean c(0,0).

In both cases the covariance matrix is presumably the identity, since
no covariance
matrix is specified.

So your final result X.1 has columns which are independent samples
from univariate
distributions, the first of which is a mixture of N(0,1) and N(3,1),
the second
of which is a mixture of N(0,1) and N(4,1), and the third and fourth
of which are
both N(0,1).

Are you really interested in

* bivariate distributions?

* mixtures of (two) univariate distributions?

* mixtures of (two) bivariate distributions?

If the latter option, why are you talking about the columns of X.1
individually?
If the middle option, why are you using rmvnorm() at all?
If the first option, what exactly is your question?

Your thinking seems to be very muddy.  You will need to clarify it
considerably.
If you do so, you may be able to pose a meaningful question, and
it yourself.

cheers,

Rolf Turner

On 23/10/2008, at 11:59 AM, Tom.O wrote:

>
> This might not be the correct forum for this question for there
> might be some
> flaws in my logic so the R function I'm looking for might not be the
> correct, but I know there’s a lot of smart people in this forum so
> correct me if I'm wrong. I have been googling and searching in this
> forum
> for something useful but so far I'm out of luck.
>
> This is the background to my problem. I have a set of samples that
> I know
> are either from a normal distribution or a bivariate normal
> distribution and
> my goal is to find the combination of samples that would give the
> best fit
> of a bivariate distribution.
>
> I'm currently using maximum likelihood estimation to fit the bivariate
> normal model but this is where my problems start. How do I find in an
> efficient way the best combination, is there a function would do
> the trick
> for me?
>
> One solution is to run an exhaustive search, but this would take a
> while
> since the possible combinations is huge. So hopefully this is my last
> option.
>
> My other problem is what test should I use to rank the models,
> WALD, F-test
> or likelihood ratio-test (LR-test)? My colleague thought that the
> LR-test
> would be the best to use, but he was not sure. And in that case which
> function is best to use. I have found some LR tests but they use
> fits from
> glm models etc.
>
> Here is an example of my problem.
> library(mixtools)
>
> x.1<-rmvnorm(40, c(0, 0))
> x.2<-rmvnorm(60, c(3, 4))
> x.3<-rmvnorm(100, c(0, 0))
> X.1<-cbind(rbind(x.1, x.2),x.3)
> colnames(X.1) =LETTERS[1:4]
>
> sample A and B is bivariate and C and D is not, so theoretically
> the best
> combination would be to use A and B in the model since they change
> at the
> same time, but other combinations with a bivariate and non bivariate
> combinations would also work but should give a worse fit than A and
> B. And
> the worst case would be to fit a bivariate distribution to C and D.
>
> So this is the case...
>
> Regards Tom
>
> --
> View this message in context: http://www.nabble.com/Help-finding-
> the-proper-function-tp20121371p20121371.html
> Sent from the R help mailing list archive at Nabble.com.
>
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> guide.html
> and provide commented, minimal, self-contained, reproducible code.

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