Abstract
Extreme value theory (EVT) asserts that the Fréchet law emerges universally from linearly scaled maxima of collections of independent and identically distributed random variables that are positive-valued. Observations of many real-world sizes, e.g. city-sizes, give rise to the Zipf law: if we rank the sizes decreasingly, and plot the log-sizes versus the log-ranks, then an affine line emerges. In this paper we present an EVT approach to the Zipf law. Specifically, we establish that whenever the Fréchet law emerges from the EVT setting, then the Zipf law follows. The EVT generation of the Zipf law, its universality, and its associated phase transition, are analyzed and described in detail.
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