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A set of K principle points of a distribution are defined as a set of k points that retain as much information as possible of the distribution in terms of mean squared distance. It provides an optimal discrete approximation to continuous distribution. This paper reviews two methods of selection of principal points and discusses their performance in asymmetric univariate continuous distributions. We propose to apply principle points in Monte Carlo simulation from two aspects: 1. Resample repeatedly from the approximate discrete distribution constituted by principle points and estimators are obtained based on the resampling points. 2. Sample points are taken by using principle points to variance reduction technique in Monte carlo. By this sampling method, the variance of unbiased estimator is proven to dramatically reduce. We use Gamma distribution and a mixture of normal distribution to demonstrate the selection of principle points and evaluate the performance of estimation when using principle points in Monte Carlo simulation. Results show that our methods can significantly improve the results obtained by the use of simple Monte Carlo simulation. This is a joint work with Min Zhou. This work is partially supported by UIC research grant No. R201409.