Corrected Discrete Approximations for the Conditional and Unconditional Distributions of the Continuous Scan Statistic

2016/02/08 by Yi‐Ching Yao, Yao, Yi-Ching, Daniel Wei‐Chung Miao +3
Computer Science · Decision Sciences · #60E05 #62E20 #Advanced Statistical Process Monitoring #Bayesian Methods and Mixture Models #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models

paper · pdf · doi:10.48550/arxiv.1602.02597

openalex publication_date 2016/02/08 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

The (conditional or unconditional) distribution of the continuous scan statistic in a one-dimensional Poisson process may be approximated by that of a discrete analogue via time discretization (to be referred to as the discrete approximation). With the help of a change-of-measure argument, we derive the first-order term of the discrete approximation which involves some functionals of the Poisson process. Richardson's extrapolation is then applied to yield a corrected (second-order) approximation. Numerical results are presented to compare various approximations.

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