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We propose a q-parameterized deterministic annealing expectation maximization (q-DAEM) algorithm for parameter estimation motivated by the concept of Tsallis entropy that originates from the nonextensive statistical mechanics. The q-DAEM algorithm combines the feature of annealing algorithms to reduce initialization sensitivity and that of q-EM algorithms to achieve fast convergence. The q-EM algorithm is a one-parameter generalized EM algorithm that has been previously proposed by the authors. By interpreting the EM algorithm via likelihood lower bound maximization, we build the fundamental interconnections among DAEM, q-DAEM, and statistical mechanics. To illustrate the benefits of using q-DAEM, we investigate two applications: finite mixture model estimation in data clustering; and joint channel estimation and data detection in communication systems, where we show that the q-DAEM algorithm achieves superior performance over the EM algorithm for both applications.