[R] Mixture of Univariate Normals

[Christian Hennig]

Dear Sharon,

the recent version of the library mclust can fit mixtures of
one-dimensional Normal distributions. It provides a decision about the
number of components by Bayesian Information criterion, too.

Did you consider a single Cauchy or t-distribution for your data? Perhaps
the tails of Normal distributions shrink too quickly for your data, so that
you would need unreasonable many Normal components?

Christian 

On Tue, 22 Oct 2002, Sharon Kuhlmann-Berenzon wrote:

> 
> Dear list,
> 
> Can anyone provide a package or code for estimating the parameters of a
> mixture of c (c >=2) univariate normal distributions?
> 
> I've tried the algorithm provided by Venables & Ripley (1999) p 263, for
> the mixture of two normal, but I don't find the "ms" function in R. I've
> used nls instead, but I'm not sure if it works the same.
> 
> The data I have is very peaked and with long tails. It should be the
> mixture of two distributions (2 types of particles), possibly with the
> same mean or very similar means. The QQ plot using the results of the VR
> algorithm (above), however, still show a clear S shape. Could this mean
> that there is yet another normal distribution in the mixture, ie c=3?
> 
> I've started the VR algorithm with different starting points, but they
> always converge to the same estimates.  I have about < 12000
> observations, and the VR algorithm converges after about 15 iterations.
> 
> Thank you for any help.
> 
> 
> Sharon Kühlmann
> 
> 
> +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
> SHARON KÜHLMANN-BERENZON
> 
> Tel. +46-31-772 53 60			Dept. Mathematical Statistics
> Fax. +46-31-772 35 08			Chalmers University of Tech.
> e-mail: sharon at math.chalmers.se		Eklandagatan 86
> 					412 96 Göteborg, Sweden
> 
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-- 
***********************************************************************
Christian Hennig
Seminar fuer Statistik, ETH-Zentrum (LEO), CH-8092 Zuerich (current)
and Fachbereich Mathematik-SPST/ZMS, Universitaet Hamburg
hennig at stat.math.ethz.ch, http://stat.ethz.ch/~hennig/
hennig at math.uni-hamburg.de, http://www.math.uni-hamburg.de/home/hennig/
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