Zipf's law unzipped

Why does Zipf's law give a good description of data from seemingly completely phenomena? Here it is argued that the reason is that they can all be as outcomes of a ubiquitous random group division: the elements can citizens of a country and the groups family names, or the elements can be the words making up a novel and the groups the unique words, or the could be inhabitants and the groups the cities in a country, and so. A Random Group Formation (RGF) is presented from which a Bayesian estimate obtained based on minimal information: it provides the best prediction for number of groups with k elements, given the total number of elements,, and the number of elements in the largest group. For each specification these three values, the RGF predicts a unique group distribution(k)\∝ exp(-bk)/k\γ, where the power-law index \γ is a function of the same three values. The universality of the result is possible by the fact that no system specific assumptions are made about mechanism responsible for the group division. The direct relation between\γ and the total number of elements, groups, and the number of elements the largest group, is calculated. The predictive power of the RGF model is by direct comparison with data from a variety of systems. It is that \γ usually takes values in the interval 1\≤\γ\≤ 2 that the value for a given phenomena depends in a systematic way on the size of the data set. The results are put in the context of earlier on Zipf's and Gibrat's laws, N(k)\∝ k⁻² and the between growth models and RGF is elucidated.