  Convolutions of independent random variables often arise in a natural way in
many applied problems. In this article, we compare convolutions of two sets of
gamma (negative binomial) random variables in the convolution order and the
usual stochastic order in a unified set-up, when the shape and scale parameters
satisfy a partial order called reverse-coupled majorization order. This partial
order is an extension of the majorization order from vectors to pairs of
vectors which also incorporates the arrangement information. The results
established in this article strengthen those known in the literature.
