Teicher [1955] proved that the probability a Poisson distribution with mean k takes on a value of k or less is monotonically decreasing in k. I extend this inequality by proving that the probability a Poisson distribution with mean zk takes on a value of k or less is monotonically decreasing for...

We propose a test of the hypothesis of stochastic monotonicity. This hypothesis is of interest in many applications. Our test is based on the supremum of a rescaled U-statistic. We show that its asymptotic distribution is Gumbel. The proof is difficult because the approximating Gaussian...