根據Huffer (1988)和Huffer and Lin (1997, 2001)所提出的遞迴關係式，我們發展出幾個特殊的演算法來計算圓周上重疊連續間隔的線性組合之聯合機率分布。我們所提出的演算法可以應用來推算多重覆蓋與掃描統計量的機率。

Based on the recursions in Huffer (1988) and Huffer and Lin (2001), and the marking algorithm in Huffer and Lin (1997), some specialized algorithms are developed.Our approach can evaluate the probabilities involving the joint distribution of overlapping sums of consecutive spacings on a circle.    Application to the distribution of circular scan statistic and multiple coverage probabilities are discussed.

1 Introduction 1
2 Recursions and Basic Properties 2
3 The Algorithm 5
4 Illustrative Example 8
5 Special Results 13
5.1 Explicit Expression for {A}1 ..............14
5.2 Explicit Expression for {A}2 ..............16
6 Concluding Remarks 17
References 18
Appendix 21

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