R help - Nov 2006 - Likelihood of multiple random processes

Is there a method in R for estimating the likelihood that two (or more) 
random variables generated a univariate sample?

For a single random variable there is:
x <- c(rnorm(20,10,3),rnorm(20,20,5))
plot(density(x))
logLik(fitdistr(x,"normal"))

Is there a way of of specifying that more than one normal distribution 
should be fitted?
If so, then I suppose that the AIC of the two models could be calculated.

Many thanks,
Dan Bebber

Department of Plant Sciences
University of Oxford

Do you know which observations came from which process (you do in your 
example, but it whatever it is supposed to emulate)?  If not, you want to 
estimate a mixture distribution.  This is covered in chapter 16 of the 
book fitdistr() supports as well as in several CRAN packages.

On Thu, 2 Nov 2006, Dan Bebber wrote:
> Is there a method in R for estimating the likelihood that two (or more)
> random variables generated a univariate sample?
>
> For a single random variable there is:
> x <- c(rnorm(20,10,3),rnorm(20,20,5))
> plot(density(x))
> logLik(fitdistr(x,"normal"))
>
> Is there a way of of specifying that more than one normal distribution
> should be fitted?
> If so, then I suppose that the AIC of the two models could be calculated.
>
> Many thanks,
> Dan Bebber
>
> Department of Plant Sciences
> University of Oxford
>
> ______________________________________________
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-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

this way the problem is not well posed. You need to place an upper
bound on the number of distributions in the mixture you want to
estimate, for otherwise the likelihood is unbounded (take one normal 
distribution for each value in your data).

----- Original Message ----- 
> Do you know which observations came from which process (you do in your 
> example, but it whatever it is supposed to emulate)?
No- I need to determine whether more than one process could have been 
involved.