Variability orderings related to coverage problems on the circle

Abstract

Suppose that n arcs with random lengths having distributions F1, F2, · ··, Fn are placed uniformly and independently on a circle. This paper presents inequalities which tell how certain distributions and probabilities change as the variability of the distributions Fl, F2, ··, Fn is increased. A distribution F is considered to be more variable than G if f h(x)dF(x) ≧ h(x)dG(x) for all convex functions h.