Is the Zipf law spurious in explaining city-size distributions?

The Zipf law, which states that that the rank associated with some size S is proportional to S to some negative power, is a regularity observed in natural and social sciences. One popular application of the Zipf law is the relationship between city sizes and their ranks. This paper examines the rank-size relationship through Monte Carlo simulations and two examples. We show that a good fit (indicated by a high R2 value) can be found for many statistical distributions. The Zipf law's good fit is a statistical phenomenon, and therefore, it does not require an economic theory that determines city-size distributions.