If a particular dataset has a lognormal distribution, will it also follow Zipf's law when the items are ranked?
That is, say I have a set of populations of a random sampling of cities (assumed to be a lognormal distribution). If I ordered them by rank, would their values be predicted by some power curve?
If so, given a mean and standard deviation of a lognormal distribution, how can I derive the power curve that Zipf's law describes?
If not, what type of distribution has the quality where when it's items are ranked, they follow Zipf's law? And also what type of curve best approximates a ranked list of items from a lognormal distribution?