Limiting sizeindex distributions for ball-bin models with Zipf-type frequencies
Limiting sizeindex distributions for ball-bin models with Zipf-type frequencies
复制标题
具有 Zipf 型频率的球仓模型的限制尺寸指数分布
DOI：
10.1007/s10463-010-0276-7
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发表时间：
2011
期刊：
影响因子：
--
通讯作者：
N. Miyoshi
中科院分区：
文献类型：
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作者：
S. Chida;N. Miyoshi
我们考虑一个随机球箱模型，其中球被随机且顺序地扔进一组箱子中。 bin 选择的频率遵循 Zipf 型（幂律）分布；也就是说，球进入第 i 个最受欢迎的 bin 的概率渐近正比于 1/iα，α> 0。在该模型中，我们推导了尺寸指数的经验分布几乎肯定收敛的极限尺寸指数分布，其中 kat timet 的尺寸指数表示恰好包含 k 个球 att 的 bin 的数量。虽然早期的研究仅处理 Zipf 型分布的幂 α 大于 1 的情况，但我们在这里考虑 α≤ 1 以及 α> 1 的情况。我们首先研究独立投掷模型的极限尺寸指数分布，然后将导出的结果扩展到独立选择 bin 的情况。模拟实验不仅证明了我们的分析是有效的，而且得出的极限分布在相对较短的时间内很好地逼近了经验规模指数分布。
We consider a random ball-bin model where balls are thrown randomly and sequentially into a set of bins. The frequency of choices of bins follows the Zipf-type (power-law) distribution; that is, the probability with which a ball enters theith most popular bin is asymptotically proportional to 1/iα,α> 0. In this model, we derive the limiting size index distributions to which the empirical distributions of size indices converge almost surely, where the size index of degreekat timetrepresents the number of bins containing exactlykballs att. While earlier studies have only treated the case where the powerαof the Zipf-type distribution is greater than unity, we here consider the case ofα≤ 1 as well asα> 1. We first investigate the limiting size index distributions for the independent throw models and then extend the derived results to a case where bins are chosen dependently. Simulation experiments demonstrate not only that our analysis is valid but also that the derived limiting distributions well approximate the empirical size index distributions in a relatively short period.