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I am new to statistics. Could somebody tell me what is the difference between a Power Law and Zipf's Law. The latter could be just for texts but I cant see any difference in their essence.

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Zipf's law is a special case of power laws, with power -1. (The harmonic series diverges, so the distribution in Zipf's law is truncated at some point. But the essential character is the point: the probabilities decline like a power of the argument.)

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"Power law" is a way of describing a general class of distributions (functions, really) that show scale invariance and slow decay in tail probabilities. Zipf's law is a specific (discrete) distribution that falls into the class of power law distributions.

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