Abstract: In this study, a distributed expectation maximization (DEM) algorithm is first introduced in a general form for estimating parameters of a finite mixture of components. This algorithm is used for density estimation and clustering of the data distributed over the nodes of a network. Then, a distributed incremental EM algorithm (DIEM) with a higher convergence rate is proposed. After a full derivation of distributed EM algorithms, convergence of both DEM and DIEM algorithms is studied based on the negative free energy concept. It is shown that these algorithms increase the negative free energy incrementally at each node until reaching the convergence. Finally, the proposed algorithms are applied to cluster analysis of gene-expression data. Simulation results approve that DIEM remarkably outperforms DEM.