Abstract
Place n arcs of equal length a uniformly at random on the circumference of a circle. We discuss the joint limit distributions of the number of gaps, the uncovered proportion of the circle and the lengths of the largest gap and of the smallest gap, depending on how a → 0 as n →∞.We show that the results may be proved in a unified and simple way by using a result of Le Cam.
Publisher
Cambridge University Press (CUP)
Subject
Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability
Reference19 articles.
1. Sur la division d'un segment par des points choisis au hasard;Levy;C.R. Acad. Sci. Paris,1939
2. The Random Division of an Interval and the Random Covering of a Circle
3. Geometric Probability
4. Un théorème sur la division d'un intervalle par des points pris au hasard;Le Cam;Publ. Inst. Statist. Univ. Paris,1958
Cited by
25 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献