Boundary crossing probabilities for the cumulative sample mean
Singham, Dashi I.
Atkinson, Michael P.
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We develop a new measure of reliability for the mean behavior of a process by calculating the probability the cumulative sample mean will stay within a given distance from the true mean over a period of time. This probability is derived using boundary-crossing properties of Brownian bridges. We derive finite sample results for independent and identically distributed normal data, limiting results for data meeting a functional central limit theorem, and draw parallels to standard normal confidence intervals. We deliver numerical results or i.i.d., dependent, and queueing processes.
The article of record may be found at https://doi.org/10.1017/S026996481700002X
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