  We compare weighted sums of i.i.d. positive random variables according to the
usual stochastic order. The main inequalities are derived using majorization
techniques under certain log-concavity assumptions. Specifically, let $Y_i$ be
i.i.d. random variables on $\mathbf{R}_+$. Assuming that $\log Y_i$ has a
log-concave density, we show that $\sum a_iY_i$ is stochastically smaller than
$\sum b_iY_i$, if $(\log a_1,...,\log a_n)$ is majorized by $(\log b_1,...,\log
b_n)$. On the other hand, assuming that $Y_i^p$ has a log-concave density for
some $p>1$, we show that $\sum a_iY_i$ is stochastically larger than $\sum
b_iY_i$, if $(a_1^q,...,a_n^q)$ is majorized by $(b_1^q,...,b_n^q)$, where
$p^{-1}+q^{-1}=1$. These unify several stochastic ordering results for specific
distributions. In particular, a conjecture of Hitczenko [Sankhy\={a} A 60
(1998) 171--175] on Weibull variables is proved. Potential applications in
reliability and wireless communications are mentioned.
