A circle covering problem and DNA breakage

Lars Holst

Statistics & Probability Letters, 1990, vol. 9, issue 4, 295-298

Abstract: Cowan, Collis and Grigg (1987) investigated a stochastic model for damage to certain types of double-stranded circular DNA. The model could be formulated as follows, Points are put at random on a circumference and marked by flipping a fair coin. Any two sufficiently close points with different marks breaks the circle. Let the random variable N be the number of points needed to get such a breakage. What can be said about N? In this paper we derive the distribution of N by a simple combinatorial argument and an approximation of it by Poisson approximation of a suitable U-statistic.

Keywords: Circle; covering; spacings; Poisson; approximation; U-statistics (search for similar items in EconPapers)
Date: 1990
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