If k is known, you can use maximun likelihood to fit the weights, means, and sd's. The EM algorithm can be of help to solve the optimization problem. You would have to implement it yourself for your particular case, but I do not think it is big trouble.
Then you could estimate k using Bayesian formalism: from a reasonable a priory distribution on k=1, 2,... compute the posterior distributions using the densities obtained above, etc.
Carlos J. Gil Bellosta Sigma Consultores Estad�sticos http://www.consultoresestadisticos.com
Joke Allemeersch wrote:
Hello,
I have a concrete statistical question:
I have a sample of an univariate mixture of an unknown number (k) of normal distributions, each time with an unknown mean `m_i' and a standard deviation `k * m_i', where k is known factor constant for all the normal distributions. (The `i' is a subscript.)
Is there a function in R that can estimate the number of normal distributions k and the means `m_i' for the different normal distributions from a sample? Or evt. a function that can estimate the `m_i', when the number of distributions `k' is known?
So far I only found a package, called `normix'. But at first sight it only provides methods to sample from such distributions and to estimate the densities; but not to fit such a distribution.
Can someone indicate where I can find an elegant solution?
Thank you in advance
Joke Allemeersch
Katholieke universiteit Leuven. Belgium.
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