Further Developments on Stochastic Dominance for Different Classes of Infinite-mean Distributions

In recent years, stochastic dominance for independent and identically distributed (iid) infinite-mean random variables has received considerable attention. The literature has identified several classes of distributions of nonnegative random variables that encompass many common heavy-tailed distributions. A key result demonstrates that the weighted sum of iid random variables from these classes is stochastically larger than any individual random variable in the sense of the first-order stochastic dominance. This paper systematically investigates the properties and inclusion relationships among these distribution classes, and extends some existing results to more practical scenarios. Furthermore, we analyze the case where each random variable follows a compound binomial distribution, establishing necessary and sufficient conditions for the preservation of the aforementioned stochastic dominance relation.