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• W2102479256 abstract "Consider a renewal process. The renewal events partition the process into i.i.d. renewal cycles. Assume that on each cycle, a rare event called 'success’ can occur. Such successes lend themselves naturally to approximation by Poisson point processes. If each success occurs after a random delay, however, Poisson convergence may be relatively slow, because each success corresponds to a time interval, not a point. In 1996, Altschul and Gish proposed a finite-size correction to a particular approximation by a Poisson point process. Their correction is now used routinely (about once a second) when computers compare biological sequences, although it lacks a mathematical foundation. This paper generalizes their correction. For a single renewal process or several renewal processes operating in parallel, this paper gives an asymptotic expansion that contains in successive terms a Poisson point approximation, a generalization of the Altschul-Gish correction, and a correction term beyond that." @default.
• W2102479256 created "2016-06-24" @default.
• W2102479256 creator A5039386346 @default.
• W2102479256 date "2001-06-01" @default.
• W2102479256 modified "2023-10-14" @default.
• W2102479256 title "Finite-size corrections to Poisson approximations of rare events in renewal processes" @default.
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• W2102479256 doi "https://doi.org/10.1239/jap/996986762" @default.
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