Abstract
In the so called lightbulb process, on days \(r=1,\ldots,n,\) out of n lightbulbs, all initially off, exactly r bulbs selected uniformly and independent of the past have their status changed from off to on, or vice versa. With \(W_n\) the number of bulbs on at the terminal time n and \(C_n\) a suitable clubbed binomial distribution,
The result is shown using Stein’s method.
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References
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Acknowledgments
The authors would like to thank the organizers of the conference held at the National University of Singapore in honor of Louis Chen’s birthday for the opportunity to collaborate on the present work.
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Goldstein, L., Xia, A. (2012). Clubbed Binomial Approximation for the Lightbulb Process. In: Barbour, A., Chan, H., Siegmund, D. (eds) Probability Approximations and Beyond. Lecture Notes in Statistics(), vol 205. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-1966-2_3
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DOI: https://doi.org/10.1007/978-1-4614-1966-2_3
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