Stochastic Monotonicity and Realizable Monotonicity

Stochastic Monotonicity and Realizable Monotonicity

We explore and relate two notions of monotonicity, stochastic and realizable, for a system of probability measures on a common finite partially ordered set (poset) S when the measures are indexed by another poset A. We give counterexamples to show that the two notions are not always equivalent, but for various large classes of S we also present conditions on the poset A that are necessary and s...

Testing for stochastic monotonicity

We propose a test of the hypothesis of stochastic monotonicity. This hypothesis is of interest in many applications in economics. 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 stochastic process contains both a stationary and a nonstationary part and so we have to extend ...

Monotonicity Properties of Stochastic Inventory Systems

Different Monotonicity Definitions in Stochastic Modelling

In this paper we discuss different monotonicity definitions applied in stochastic modelling and discuss the relationships between them. Obviously, the monotonicity concept depends on the relation order that we consider on the state space. In the case of total ordering the stochastic monotonicity used in stochasticmodelling and the realizablemonotonicity used in perfect simulation are equivalent...

Stochastic Monotonicity in Intergenerational Mobility Tables

The aim of this paper is to test for stochastic monotonicity in intergenerational socio-economic mobility tables. In other words we question whether having a parent from a high socio-economic status is never worse than having one with a lower status. Using existing inferential procedures for testing unconditional stochastic monotonicity, we first test a set of 149 intergenerational mobility tab...