R help - Apr 2009 - finite mixture model (2-component Weibull): plotting Weibull components?

Dear Knowledgeable R Community Members,
 
 Please excuse my ignorance, I apologize in advance if this is an easy question,
but I am a bit stumped and could use a little guidance.
 
 I have a finite mixture modeling problem -- for example, a 2-component Weibull
mixture -- where the components have a large overlap, and
 I am trying to adapt the "mclust" package which concern to normal
mixture to solve this problem.
 
 I need to decompose that mixture into its 2 components which will need to be
plotted.
 
 What I don't know how to do is:
 
 (1) restrict the number of components to 2 .
 
 (2) obtain and plot a component Weibull density 
 
 (Note: my real dataset will not have peaks this well separated, but I needed to
find a small example.)

Any information you might be able to shed on this would be very much appreciated
With appreciation for your help.

Thank you in advance

Cordially;
 Abdoul Aziz Junior NDOYE
 GREQAM Marseille.



      
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mclust doesn't do Weibull mixtures, only Gaussian ones (though you may 
approximate a Weibull by several Gaussians). You may look up the flexmix 
package, which either does it already or a method function can be provided
to do it.
There is also an example "fitting a mixture distribution" in Venables
and
Ripley's MASS book with normals (including plotting the density), which 
you could adapt for Weibull distributions by plugging in the 
corresponding functions for the Weibull.
> (1) restrict the number of components to 2 .
Specify G=2 in mclust (if want to fit 2 Gaussians).
> (2) obtain and plot a component Weibull density
Generally, adding a Weibull mixture density to a plot works by

x <- seq(0,100,by=0.1)
# or whatever reasonable choice of x-values
lines(x,p*dweibull(x,s11,s12)+(1-p)*dweibull(x,s21,s22))

where p, s11, s12, s21, s22 are the mixture parameters.

Regards,
Christian

*** --- ***
Christian Hennig
University College London, Department of Statistical Science
Gower St., London WC1E 6BT, phone +44 207 679 1698
chrish at stats.ucl.ac.uk, www.homepages.ucl.ac.uk/~ucakche