The Dominant Relations and Their Applications on Some Subclasses of Heavy-Tailed Distributions

We’ve obtained the equivalent condition of the distributions which can dominate all light-tailed distributions, as well as those which can dominate all light-tailed distributions and lightly heavy-tailed distributions. We discuss the dominant relations between distrbutions and their corresponding equilibrium distributions. We also give some applications in the closure of sums based on some dominant correlations above-mentioned.