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In this paper, to achieve high-quality speech enhancement, we introduce the generalized minimum mean-square error short-time spectral amplitude estimator with a new blind prior estimation of the speech probability density function (p.d.f.). To deal with various types of speech signals with different p.d.f., we propose an algorithm of speech kurtosis estimation based on moment-cumulant transformation for blind adaptation to the shape parameter of speech p.d.f. From the objective and subjective evaluation experiments, we show the improved noise reduction performance of the proposed method.