Clubbed Binomial Approximation for the Lightbulb Process

2011/11/16 by Goldstein, Larry, Xia, Aihua
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1111.3984

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) ≤ 2.7314 √(n) e^-(n+1)/3 for all n ≥ 1. The result is shown using Stein's method.

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