A generalized finite mixture model for asymmetric probability distribution observations

Finite mixture model is a useful probabilistic model for representing the probability distributions of observations. Gaussian mixture model (GMM) is a widely used one whose parameters are always estimated by the famous EM algorithm. But when probability distributions contain asymmetric modes, GMM requires much more constituent components to achieve a satisfied accuracy. Therefore, a generalized mixture finite model is proposed. First, it adopts the derivative Formula: see text-PDF which can well represent the asymmetric probability distributions as the probability density. However, the differential operation and solving the likelihood equations are scarcely possible in the M step of EM algorithm for the complex expression of the derivative Formula: see text-PDF. Second, a pseudo EM method is proposed to avoid the abovementioned difficulty which finds the pseudo maximum likelihood estimates of the parameters by utilizing the moment matching principle. It more easily estimates the parameters by solving a series of moment matching equations. Finally, four examples are presented to verify that the proposed generalized finite mixture model has advantage on representing the asymmetric probability distributions observations.