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In this paper, we present a new statistical technique for estimation of average power dissipation in digital circuits. The present parametric statistical technique estimates the average power based on the assumption that the power distribution can be characterized by a preassumed function. Large error can incur when the assumption is not met. On the other hand, the existing nonparametric technique, although accurate, is too conservative and requires a large sample size in order to achieve convergence. For a good tradeoff between simulation accuracy and computational efficiency, we propose a new nonparametric technique using the properties of the order statistics. It is generally applicable to any type of circuit irrespective of its power distribution function. Compared to the existing nonparametric technique, it is much more computationally efficient since it requires a much smaller sample size to achieve the same accuracy specification. This new technique is implemented in the distribution-independent power estimation tool (DIPE). DIPE is empirically demonstrated to be more robust and accurate than the parametric technique.