Efficient tail estimation for massive correlated log-normal sums — with applications in statistical leakage analysis

Existing approaches to statistical leakage analysis focus only on calculating the mean and variance of the total leakage. In practice, however, what concerns most is the tail behavior of the sum distribution, as it tells that to what extent the design will be safe or reliable. However, computing the tail distribution is much more difficult than computing the mean and variance. In this paper, we tackle this problem by making use of the recent developments in the area of financial and insurance analysis, as well as the fast evaluation algorithm for the variance of spatially correlated random sums. The proposed algorithm is provably of O(N) complexity. Experiments show that the algorithm provides 1% accuracy in modeling the tail behavior and it is 10X more accurate compared with existing methods that approximate the distribution by matching the moments of a lognormal distribution.