Approximate circuit design has gained significance in recent years targeting error tolerant applications. In this paper, we consider the problem of minimizing the power for a given
accuracy, in a signal processing application with accurate adders replaced by low-power approximate adders. We first demonstrate that the commonly used assumption that the inputs to the adder are uniformly distributed results in an inaccurate prediction of error statistics for multi-level circuits. To overcome this problem, we propose the use of parameterized error models for adders, with input static probabilities as parameters. The static probability computation in our work considers not just the functionality of the adder but also its position in the circuit, functionality of its parents and the number of approximate bits in the parent blocks. This parameterized error model can be incorporated in any optimization framework. We demonstrate up to 6.5 dB improvement in the accuracy of noise power prediction when the proposed model is used to optimize an 8x8 DCT.