[R] Mixture of Univariate Normals

[Ben Bolker]

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.

  optim() is a closer analogue, but if you're assuming normal 
distributions you should be able to reduce your problem to one that can be 
handled by least-squares (nls).

See the on-line complements, 
http://www.stats.ox.ac.uk/pub/MASS3/Compl.shtml, under chapter 8 the R 
complements say:

Function nls is in standard package nls . Most of the optimization 
examples can be done using nlm or optim , but symbolic differentiation 
using deriv does not work for our examples. See the script ch08.R for 
details.

> 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?

  Actually it sounds more like a mixture of t-distributions to me.  I'd 
take a shot at modifying the VR algorithm accordingly.  (Although I would 
note that if the means are very similar you may have some trouble 
identifying the mixture ...)

> 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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