[R] Fitting & evaluating mixture of two Weibull distributions

jones jones at reed.edu
Mon Mar 5 16:50:16 CET 2012

The contribution of each observation to the logliklihood is
            log(p*f1(x) + (1-p)*f2(x))
where f1 and f2 are the two density functions.   Just sum.

  The standard likelihood ratio test is problematic here, as there
are two parametrizations that reduce the mixture model to a single
component: p=1 vs p < 1 plus the shape and scale parameters
of the two components are identical.


On 3/5/12 2:57 AM, N.Alberts at roehampton.ac.uk wrote:
> Hello,
> I would like to fit a mixture of two Weibull distributions to my
> data, estimate the model parameters, and compare the fit of the model
> to that of a single Weibull distribution.
> I have used the mix() function in the 'mixdist' package to fit the
> mixed distribution, and have got the parameter estimates, however, I
> have not been able to get the log-likelihood for the fit of this 
> model
> in order to compare it to the single distribution.
> I have also had a look at the 'Mixtools' and 'Flexmix' packages. With
> both of these it is possible to fit a mixture of distributions, but,
> as far as I can tell, these are pre-defined and do not have a 
> function
> for a mixture of two Weibull distributions.
> I have used the 'fitdistrplus' package to fit the single 
> distribution.
> Does anyone have any suggestions either for getting the
> log-likelihood for models fitted with the mix() function, or other
> packages / functions which allow me to fit a double Weibull and get
> the log-likelihood for the model?
> Any suggestions are much appreciated!
> Best wishes,
> Nienke
> ----------------------------------------------------------------------------------------------
> Nienke Alberts
> PhD Candidate
> Centre of Research in Evolutionary & Environmental Anthropology
> University of Roehampton
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