Clubbed Binomial Approximation for the Lightbulb Process

Larry Goldstein; Aihua Xia

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arXiv · 1111.3984

Clubbed Binomial Approximation for the Lightbulb Process

Larry Goldstein·Aihua Xia

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Abstract

In the so called lightbulb process, on days r=1,..,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, d_{TV}(W_n,C_n) \le 2.7314 \sqrt{n} e^{-(n+1)/3} for all n \ge 1. The result is shown using Stein's method.

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Larry Goldstein, Aihua Xia. 2011-11-16. Clubbed Binomial Approximation for the Lightbulb Process. https://arxiv.org/abs/1111.3984

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