This paper obtains Lorenz ordering relationships among order statistics from log-logistic samples of possibly different sizes. Some results extend other families including the Lomax, Burr III and Burr XII distributions.

The paper explores the relationship between various orderings among probability forecasts that have been suggested in the literature. It is shown that well calibrated forecasters are in general not comparable according to the domination ordering suggested by Vardeman and Meeden (1983), that the...