Random arcs on the circle
- 1 December 1978
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 15 (4), 774-789
- https://doi.org/10.2307/3213433
Abstract
Place n arcs of equal lengths randomly on the circumference of a circle, and let C denote the proportion covered. The moments of C (moments of coverage) are found by solving a recursive integral equation, and a formula is derived for the cumulative distribution function. The asymptotic distribution of C for large n is explored, and is shown to be related to the exponential distribution.Keywords
This publication has 8 references indexed in Scilit:
- Covering the circle with random ARCSIsrael Journal of Mathematics, 1972
- Moments of coverage and coverage spacesJournal of Applied Probability, 1966
- The Random Division of an Interval and the Random Covering of a CircleSIAM Review, 1962
- On a Class of Problems Related to the Random Division of an IntervalThe Annals of Mathematical Statistics, 1953
- The problem of random intervals on a lineMathematical Proceedings of the Cambridge Philosophical Society, 1947
- The Probability Distribution of the Measure of a Random Linear SetThe Annals of Mathematical Statistics, 1946
- On the Measure of a Random SetThe Annals of Mathematical Statistics, 1944
- SOLUTION TO A GEOMETRICAL PROBLEM IN PROBABILITYAnnals of Eugenics, 1939