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On the polygon generated by n random points on a circle

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  • Bélisle, Claude

Abstract

Let An denote the surface area of the random polygon generated by n independent points uniformly distributed on the unit circle in . We investigate the asymptotic properties of An. In particular, we show that , and that the distribution of is asymptotically normal. Similar results are obtained for the perimeter. As a byproduct of this investigation, we give a simple proof of a general convergence theorem for sums of powers of the spacings in a sample from the uniform distribution on an interval.

Suggested Citation

  • Bélisle, Claude, 2011. "On the polygon generated by n random points on a circle," Statistics & Probability Letters, Elsevier, vol. 81(2), pages 236-242, February.
  • Handle: RePEc:eee:stapro:v:81:y:2011:i:2:p:236-242
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