Disclosed are embodiments of a method and an associated computer program product for finding the statistical bounds, the corresponding parameter corners and the probability density function of one or more performance targets for a circuit without requiring Monte Carlo simulation runs. To accomplish this, a joint probability density function for independent parameters that affect the performance target can be constructed. Then, based on the joint probability density function, the statistical bounds of the performance target can be found by constructing an equal-probability-density surface of the joint probability density function and solving a constrained optimization problem on that equal-probability-density surface. Once the statistical bounds are determined, the corresponding parameter corners for the performance target can also be determined. After obtaining multiple statistical bounds corresponding to different accumulated probability density, the probability density function of the performance target can also be obtained.