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Zipf's law is a fundamental paradigm in the statistics of written and spokennatural language as well as in other communication systems. We raise thequestion of the elementary units for which Zipf's law should hold in the mostnatural way, studying its validity for plain word forms and for thecorresponding lemma forms. In order to have as homogeneous sources as possible,we analyze some of the longest literary texts ever written, comprising fourdifferent languages, with different levels of morphological complexity. In allcases Zipf's law is fulfilled, in the sense that a power-law distribution ofword or lemma frequencies is valid for several orders of magnitude. Weinvestigate the extent to which the word-lemma transformation preserves twoparameters of Zipf's law: the exponent and the low-frequency cut-off. We arenot able to demonstrate a strict invariance of the tail, as for a few textsboth exponents deviate significantly, but we conclude that the exponents arevery similar, despite the remarkable transformation that going from words tolemmas represents, considerably affecting all ranges of frequencies. Incontrast, the low-frequency cut-offs are less stable.

Zipf's law for word frequencies: word forms versus lemmas in long texts