  A stochastic ordering approach is applied with Stein's method for
approximation by the equilibrium distribution of a birth-death process. The
usual stochastic order and the more general s-convex orders are discussed.
Attention is focused on Poisson and translated Poisson approximation of a sum
of dependent Bernoulli random variables, for example k-runs in i.i.d. Bernoulli
trials. Other applications include approximation by polynomial birth--death
distributions.
