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Adaptive resource allocation has been shown to provide substantial performance gain in OFDMA-based wireless systems, such as WiMAX, when full channel state information (CSI) is available at the transmitter. However, in some fading environments (e.g., fast fading), there may not be a feedback link sufficiently fast to convey the CSI to the transmitter. In this paper, we consider resource allocation strategies for downlink multiuser mobile WiMAX systems, where the transmitter has only the channel distribution information (CDI), but no knowledge of the instantaneous channel realization. We address the problem of subchannel assignment and power allocation, to maximize the ergodic weighted-sum rate under long-term fairness, minimum data rate requirement and power budget constraints. This problem is formulated as a nonlinear stochastic constrained optimization problem. We provide an analytical solution based on the Lagrange dual decomposition framework. The proposed method has a complexity of ðÂ’ª(KM) for K users and M subchannels. Simulation results are provided to compare the performance of this method with other allocation schemes and to illustrate the tradeoff between maximized weighted-sum rate and the constraints.