流行的统计规律：电影票房动态的普遍属性
The statistical laws of popularity: Universal properties of the box office dynamics of motion pictures
摘要：
相对于其他（通常是质量相似的）竞争对手，某些产品或想法变得流行的过程是否有一般性的原则？为了详细研究这个问题，我们把重点放在电影的受欢迎程度上，以票房收入来衡量。我们观察到，对数正态分布很好地描述了总收入、首映周收入以及每家影院每周收入的经验分布的尾部（对应于最成功的电影）。这一观察结果表明，受欢迎程度可能是一个线性乘法随机过程的结果。此外，总收入和首映收入的分布呈现双峰形式，大多数电影在影院的表现要么很好，要么很差。我们还观察到，平均而言，电影在其生命周期中的任何时候，每个影院的总收入与其发行后的时间成反比。我们认为，（i）尾部的对数正态性质，（ii）总体总收入分布的双峰形式，以及（iii）每个剧院的总收入随时间的幂律衰减，构成了{ \em程式化事实}的基本集合（即，经验“定律”），可以用来解释关于电影流行度的其他观察。我们表明，结合一个固定的较低的截止收入的假设，低于电影从电影院撤回，这些法律可以用来推导出Weibull分布的生存概率的电影同意与经验数据。与极值分布的联系表明，流行度可以被视为一个过程，在这个过程中，产品通过避免失败而变得流行（即，从流通中退出）许多连续的时间段。我们认为，这些结果可能适用于一般的流行。
英文摘要：
Are there general principles governing the process by which certain products or ideas become popular relative to other (often qualitatively similar) competitors? To investigate this question in detail, we have focused on the popularity of movies as measured by their box-office income. We observe that the log-normal distribution describes well the tail (corresponding to the most successful movies) of the empirical distributions for the total income, the income on the opening week, as well as, the weekly income per theater. This observation suggests that popularity may be the outcome of a linear multiplicative stochastic process. In addition, the distributions of the total income and the opening income show a bimodal form, with the majority of movies either performing very well or very poorly in theaters. We also observe that the gross income per theater for a movie at any point during its lifetime is, on average, inversely proportional to the period that has elapsed after its release. We argue that (i) the log-normal nature of the tail, (ii) the bimodal form of the overall gross income distribution, and (iii) the decay of gross income per theater with time as a power law, constitute the fundamental set of {\em stylized facts} (i.e., empirical "laws") that can be used to explain other observations about movie popularity. We show that, in conjunction with an assumption of a fixed lower cut-off for income per theater below which a movie is withdrawn from a cinema, these laws can be used to derive a Weibull distribution for the survival probability of movies which agrees with empirical data. The connection to extreme-value distributions suggests that popularity can be viewed as a process where a product becomes popular by avoiding failure (i.e., being pulled out from circulation) for many successive time periods. We suggest that these results may apply to popularity in general.
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