A two-stage algorithm for computation of the exact distribution of sums of spacings

ABSTRACT

Based on the recursions in Huffer (1988) and Huffer and Lin (2001), we present a two-stage algorithm and two specialized methods for evaluating the probabilities involving linear combination of spacings of special forms. The two-stage algorithm combines the advantages of marking algorithm in Huffer and Lin (1997) and general algorithm in Huffer and Lin (2001). The proposed methods can analytically derive the exact expressions for some specific problems, and efficiently handle problems such as the distribution of the circular scan statistic and multiple coverage probabilities.

KEYWORDS:

• Circular scan statistic
• Multiple coverage problems
• Symbolic computation

MATHEMATICS SUBJECT CLASSIFICATION:

• 62E15
• 62P30

Acknowledgments

We express our sincere thanks to the Associate Editor and the anonymous referee for their valuable comments and suggestions. This work was partially supported by the Ministry of Science and Technology of the Republic of China, Taiwan (104-2118-M-032-001-MY2).