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<Paper uid="W98-1218">
  <Title>Applications and Explanations of Zipf's Law</Title>
  <Section position="4" start_page="7" end_page="7" type="concl">
    <SectionTitle>
4. Conclusions
</SectionTitle>
    <Paragraph position="0"> At this stage, only tentative conclusions can be made from this preliminary studies, although further investigations are being undertaken using larger corpora in multiple languages. Zipf's theory requires effort to be constant independent of frequency, however Information Theory and Psychological experiments both indicate that this ought not to be the case, and that it in fact decreases in a way consistent with an optimal strategy for an unbounded lexicon. We have not been able to establish the validity of an optimum sample size for a particular corpus, genre or lexicon, but observe that new words tend to enter faster than they repeat, as evidenced by the fact that the number of words of frequency 1 tends to increase Powers 159 Applications and Explanations of Zipfls Law  as the size of sample increase. Given that language is productive, and an unbounded lexicon model has been indicated (or at least possible) in each of our experiments, this trend may well continue indefinitely, although it does seem to slow as the sample is increased (even though we increase by doubling).</Paragraph>
  </Section>
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