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Synthetic data, when properly used, can enhance patterns in real data and thus provide insights into different problems. Here, the estimation of tail probabilities of rare events from a moderately large number of observations is considered. The problem is approached by a large number of augmentations or fusions of the real data with computer-generated synthetic samples. The tail probability of interest is approximated by subsequences created by a novel iterative process. The estimates are found to be quite precise., Competing Interests: Conflict of interestThe authors declare that there is no conflict of interest., (© Grace Scientific Publishing 2021.)

The probability that mortality from certain causes exceeds high thresholds is addressed. An out-of-sample fusion method is presented where an original real data sample is fused or combined with independent computer-generated samples in the estimation of exceedance probabilities assuming a density ratio model. Since the size of the combined sample of real and artificial data is larger than that of the real sample, the fused sample produces short confidence intervals relative to traditional methods. Numerical results show that the method maintains good coverage even for some misspecified cases.