# Number of parameters mixture model

In order to do a LRT between two mixture models with different numbers of components, I need to know the number of parameters. I would like to know the answer both for: a) Gaussian mixture model b) Betabinomial mixture model

I read that for mixtures of Gaussians the number of parameters is 3k-1 (k being the number of components). Where does this number come from?

Thanks!

• k means, k variances, and k weights that sum up to one, hence of effective dimension k-1 – Xi'an Mar 26 '18 at 11:19

If there are no restrictions on the parameters of the components of a finite mixture model, then the only restriction is that the mixture weights should sum to one. Hence the total number of independent parameters in a $k$-mixture is:
$k*$(num of parameters of each component) $+ k-1$.
Since the Gaussian has 2 parameters the answer to a) is $3k-1$.
The BetaBinomial distribution is not a finite mixture model and has 2 parameters (if the number of trials $n$ is known)