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In this work, the speech spectrum source is modeled. The spectrum is represented by the cepstral coefficients resulting from linear prediction analysis of speech. The models are Gaussian mixture densities, estimated iteratively using two expectation maximization type algorithms. The contribution is an investigation of the algorithms using theoretical measures well as practical applications. The applications are spectrum coding and prediction. Some low-dimensional modeling examples, illustrating the behavior of the two algorithms graphically are given. One of the algorithms has the bounded support issue of the source incorporated in its update equations, resulting in improved modeling accuracy.