I am trying to fit my data with a bimodal distribution using two beta distributions, however it seems to me that the two peaks are not captured very well. The reason that I notice from the data is that it has too many zeros and 100s. I had tried to use mixtool, gamlss and flexmix in R but none of them provided me a satisfactory fitting. Mostly, they have problem with convergence. Thus, I wrote my own EM algorithm to fit it and fortunately it can be fitted using two betas or two normals (please see attached). I have the following questions:

  1. With this type of distribution (bimodal and high point mass around each peaks), what is the best mixture model to fit and respective algorithm, EM, etc.?
  2. Rather than mixtool, gamlss and flexmix pakages, is there any other that can be used to fit the bimodal distribution?

I am looking forward to hearing your advice and experience.

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  • $\begingroup$ Why do you use only two components? Judging from your histogram, there should be at least four, because of the huge peak at zero and 100. I am also surprise you use a Beta mixture given the range of the data. If you have repeated observations at exactly zero and 100, point masses at those values should be part of the model. $\endgroup$ – Xi'an Nov 11 '16 at 6:52
  • $\begingroup$ Hi Xi'an, thank you very much for your comments. I have tried three mixtures as well but unfortunately the fitting is not as good as two. When using the gamlss.mix I also tried 4 and 5 mixtures but got problem with convergence of the EM algorithm. Here I used the generalised beta distribution in a particular interval not necessary between 0 and 1. $\endgroup$ – Philippe Nov 14 '16 at 1:59

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