Patent ID: 8175830

Claim:
A computer-implemented method for estimating a magnitude of extremely rare events upon receiving a complete data sample representing past events over a time period and a specific exceedance probability, the method comprising: choosing, by a computing system including at least one memory device and at least one processor connected to the at least one memory device, a distribution of the complete data sample; fitting, by the computing system, the distribution to subsamples of the complete data sample; performing, by the computing system, a goodness-of-fit test to determine whether a subsample is fitted to the distribution; setting, by the computing system, a subsample as an acceptable subsample, if a result of the goodness-of-fit test of the subsample is higher than a predetermined threshold; estimating, by the computing system, a tail weight of the acceptable subsample; evaluating, by the computing system, whether the estimated tail weight of the acceptable subsample lies outside a confidence interval of a subsample that is smaller than the acceptable subsample and that is fitted to the distribution; setting, by the computing system, the acceptable subsample as an unacceptable subsample, if the estimated tail weight of the acceptable subsample lies outside the confidence interval; setting, by the computing system, a subsample as the unacceptable subsample, if the result of the goodness-of-fit test of the subsample is less than or equal to the predetermined threshold; identifying, by the computing system, an optimal subsample that is a largest acceptable subsample among acceptable subsamples fitted to the distribution of the complete data sample; and computing, by the computing system, a quantile estimate based on the optimal subsample and the specific exceedance probability, the quantile estimate indicating the magnitude of the extremely rare events.