Random Walks of Ordered Elements with Applications

In this partly expository paper a simple random walk model is introduced for generating sequences of ordered elements.The model is related to Pólya's urn scheme.An alternative description of the walk leads to conditionally independent steps.A basic theorem for the walk is proved and applications are given.Among other things, recursion formulas for moments of order statistics are studied and connections with exceedances and distribution-free tolerance intervals are indicated.