Power-law distribution (Pareto)& Zipf's Law: connection and how to fit the distribution of global city population
- This post counts for 3 days. - In short, We use the histogram to outline the distribution, use rank-frequency plot (log-log plot) to identify the power-law distribution, and use maximum likelihood estimation to obtain the parameters. - I will show 1 st , how the power-law function CDF and PDF can be derived from Zipf CDF; and 2 nd , this least square estimation by excel is wrong and how to get the right one. Historical background on the power-law distribution. - Power-law distribution is as common as normal distribution in the real world. In the 19 th century, Italian economist Pareto realized that 20% of the population owns 80% the wealth, which is the famous 80/20 rule. He later named the power-law distribution as Pareto distribution, which is what we studied in the probability course. - In the 20 th century, another main contributor, Zipf made a similar discovery in linguistics about the frequency of words used. - Besides social wealth, many things fol...