Boundary crossing probabilities for the cumulative sample mean
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Authors
Singham, Dashi I.
Atkinson, Michael P.
Subjects
applied probability
reliability theory
simulation
brownian bridge
Brownian bridge
reliability
reliability theory
simulation
brownian bridge
Brownian bridge
reliability
Advisors
Date of Issue
2018
Date
2018
Publisher
Language
en_US
Abstract
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 dis- tributed normal data, limiting results for data meeting a functional central limit theorem, and draw parallels to standard normal confidence intervals. We deliver numerical results for i.i.d., dependent, and queueing processes.
Type
Article
Description
The article of record may be found at https://doi.org/10.1017/S026996481700002X
Series/Report No
Department
Operations Research (OR)
Organization
Naval Postgraduate School (U.S.)
Identifiers
NPS Report Number
Sponsors
Funder
Format
Citation
Singham, Dashi I., and Michael P. Atkinson. "Boundary crossing probabilities for the cumulative sample mean." Probability in the Engineering and Informational Sciences 32.2 (2018): 275-295. doi:10.1017/S026996481700002X
Distribution Statement
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.