Web Science/Part2: Emerging Web Properties/Advanced statistical descriptive models for the Web

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Advanced statistical descriptive models for the Web

Learning goals

  1. fitting a curve
  2. work with logarithmic plots
  3. zipfs law
  4. power law

Associated units

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  1. Be able to name some fundamental properties about how frequencies of words in texts are distributed
  2. Be a little bit more cautious about visual impressions when looking at log-log plots
  3. Know both formulations of Zipf’s law
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  • Be able to do a coordinate transformation to change the scales of your plots
  • Understand in which scenario power functions appear as straight lines
  • Know in which scenarios exponential functions appear as straight lines
  • Be even more cautious about your visual impressions
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  • Know the axioms for a distance measure and how they relate to norms.
  • Know at least two distance measures on functions spaces.
  • Understand why changing to the CDF makes sense when looking at distance between functions.
  • Understand the principle of the Kolomogorov-Smirnov test for fitting curves
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  • Know how to transform a rank frequency diagram to a powerlaw plot.
  • Understand how powerlaw and pareto plots relate to each other.
  • Be able to explain why a pareto plot is just and inverted rank frequency diagram
  • Be able to transform the zipf coefficient to the powerlaw and pareto coefficient and vice versa.
  • Understand that building the CDF is basically like building the integral.
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