# 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

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
• 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
• 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
• 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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