[R] Mixture of Univariate Normals

[ripley@stats.ox.ac.uk]

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

> Can anyone provide a package or code for estimating the parameters of a
> mixture of c (c >=2) univariate normal distributions?

Alternatives include packages mclust and mda.

> 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.

Try Venables & Ripley (2002) instead, or even look in the R scripts
in the MASS library, specifically the MASS/scripts/ch16.R file.
(The version for the 1999 book is MASS/scripts/ch08.R.)

> 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?

Well, a mixture of two normals is not long-tailed, so I think you need
something else, e.g. a mixture of t's.

-- 
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 272860 (secr)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595


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