We present a low computational cost bit allocation procedure dedicated to wavelet compression performed by entropy coded lattice vector quantization (ECLVQ). It is based on a previously proposed statistical model called multidimensional mixture of generalized Gaussian densities. Here, we focus on the distribution estimation step which requires to be as fast as possible. We show that the method of moments can be used successfully as an alternative to Monte Carlo Markov chain approach (MCMC) ; this method allows not only to reduce the computational complexity but also to maintain a good estimation performance. Experimental results show the efficiency of our approach in terms of CPU time.