It turns out that some empirical facts in Big Data are the effects of properties of large numbers. Zipf's law 'noise' is an example of such an artefact. We expose several properties of the power law distributions and of similar distribution that occur when the population is finite and the rank and counts of elements in the population are natural numbers. We are particularly concerned with the low-rank end of the graph of the law, the potential of noise in the law, and with the approximation of the number of types of objects at various ranks. Approximations instead of exact solutions are the center of attention. Consequences in the interpretation of Zipf's law are discussed.

翻译：研究表明，大数据中的某些经验事实是巨大数性质的体现。齐普夫定律的"噪声"正是此类人为现象的典例。我们揭示了当总体有限且总体中元素的秩次与计数均为自然数时，幂律分布及类似分布的若干特性。我们特别关注该定律图形中低秩端、定律中的潜在噪声，以及不同秩次下对象类型数量的近似计算。本文核心聚焦于近似解而非精确解，并探讨了这些结论对齐普夫定律解读的影响。