Best upper quantile evaluations for NWU distributions (Q1871220)

Let \( W \) be a fixed distribution function, and let \(\mathcal{F}_W\) be the family of distributions that are larger than, or equal to \(W \), in the superadditive stochastic order, and that have a finite mean \(\mu \) and variance \(\sigma^2\). The author obtains optimal upper bounds on quantiles in the family \(\mathcal{F}_W\), and identifies the distributions that attain the bounds. In particular, he provides explicit bounds on quantiles of new worse than used (NWU) distributions, and shows that they are attained by geometric distributions.