Abstract
In this study, Monte-Carlo simulation samples are generated by the periodic Gibbs sampling algorithm. The probability of a rare event will be estimated from these simulated samples. By using the Naïve Monte Carlo method to estimate the very small probability of rare events, it is necessary to create very large simulation samples that take a long time to initialize. This limitation was significantly improved by combining the cross-entropy method with the Gibbs sampling algorithm to create Monte-Carlo simulation samples. Using the technique of probability measure change in the cross-entropy method, rare events will occur in the simulation sample at a higher frequency according to the new probability measure. The probability of these rare events can be well estimated by returning the results for the initial probability measure.
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