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Conventional ICA algorithms typically model the probability density functions of the underlying sources as highly kurtotic or symmetric. However, when source data violate the assumptions (e.g. low kurtosis), the conventional ICA methods might not work well. Adaptive modeling of the underlying sources thus becomes an important issue for ICA applications. This paper proposes the log Weibull model to represent skewed distributed sources within the infomax framework and further introduces an adaptive ICA method. The central idea is to use a two-stage separation process: 1) conventional ICA used for all channel sources to obtain initial independent source estimates; 2) source density estimate-based nonlinearities adaptively used for the "refitting" separation to all channel sources. The ICA algorithm is based on flexible nonlinearities of density matched candidates. Our simulations demonstrate the effectiveness of this approach.