On the polygon generated by n random points on a circle

Claude Bélisle

Statistics & Probability Letters, 2011, vol. 81, issue 2, 236-242

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.

Keywords: Random; convex; hull; Central; limit; theorem; Cramer's; theorem; Spacings (search for similar items in EconPapers)
Date: 2011
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