In modern circuit design, it is difficult to provide reliable parametric yield prediction since the real distribution of process data is hard to measure. Most existing approaches are not able to handle the uncertain distribution property coming from the process data. Other approaches are inadequate considering correlations among the parameters. This paper suggests a new approach that not only takes care of the correlations among distributions but also provides a low cost and efficient computation scheme. The proposed method approximates the parameter variations with Chebyshev Affine Arithmetics (CAA) to capture both the uncertainty and the nonlinearity in Cumulative Distribution Functions (CDF). The CAA based probabilistic presentation describes both fully and partially specified process and environmental parameters. Thus we are capable of predicting probability bounds for leakage consumption under unknown dependency assumption among variations. The end result is the chip level parametric yield estimation based on leakage prediction. The experimental results demonstrate that the new approach provides reliable bound estimation while leads to 20% yield improvement comparing with interval analysis.