Modelling irregular and multimodal tree diameter distributions by FMM

Today, I read the paper 'Modelling irregular and multimodal tree diameter distributions by FMM'. It introduced an application of FMM to realistic problems. I think it is really helpful for my research. I sketched the logic of this whole method.

Summary:
There are a few steps to apply FMM to modelling irregular and multimodal tree diameter distributions:
1. select database as samples
2. select regular distributions

the upper one is Weibull distribution and the other is gamma distribution.
The finite mixture dnesity functions consisting of two or three Weibull distributions and two or three gamma distributions can be written as

the upper one is k=2 and the other is k=3.
3. use multistart method (MM) to choose initial parameter values (weights and components)
4. estimate the parameters of the mixture model using MLE
5. apply MLE by using EM algorithm with a Newton-type (NT) method to optimize the parameters
6. evaluate the fitting results by p value of chi-square test, bias and RMSE

I think they could be applied to my research.

Tomorrow, I will try to find corresponding codes in Matlab to realize the logic. There are many related packages in Matlab and I think I can find them in Matlab.