A method and system for estimating a magnitude of extremely rare events upon receiving a complete data sample and a specific exceedance probability are described. A distribution is chosen for a complete data sample. An optimal subsample fitted to the distribution is obtained. The optimal subsample is a largest acceptable subsample. A subsample is considered as an acceptable subsample when a goodness-of-fit test on the subsample is satisfactory (i.e., higher than a predetermined threshold). In addition, if a tail measure of an acceptable subsample lies outside a confidence interval of any smaller acceptable subsample, the acceptable subsample is considered as an unacceptable. Based on the optimal subsample and an inputted exceedance probability, a quantile estimate is computed, e.g., by executing an inverse of a cumulative distribution function of generalized Pareto distribution.