Statistics and Data Analysis

Yesterday I basically said a distribution that can satisfy Zipf's law is a Pareto distribution. I need to clarify that Zipf's law is not the same as power-law. Zipf's law simply relies on the fact that the slope in log-log rank-to-size is approximately 1. So the population size of a city is inversely proportional to the rank of the size of the city. For example, in the US, the tenth-ranked city, Detroit, should have a size of 1/10 of New York. Today I was reading a good paper by Jan Eeckhout (2004): "Gibrat's law for all cities". He fit the distribution on the US 2010 census data on 25,359 cities, towns and villages ranging from 1 to over 8 million in population, and show power-law only fit for cities larger than a certain lower boundary. The lognormal distribution would fit the entire population (fit means KS test doesn't reject with 5% significance level). The two fitted distribution are more similar when the size is over Exp(12), which is 160 thousand...

The Uppsala Conflict Data Program (UCDP) has recorded ongoing violent conflicts since the 1970s. Using its dataset of 135 thousand records of organized violence globally since 1989, we can evaluate the distribution of conflicts in the world and in specific countries. I listed here the top 10 countries: Order Country Freq 1 Afghanistan 22,726 2 India 14,465 3 Iraq 6,488 4 Nepal 5,652 5 Pakistan 5,528 6 Turkey 4,826 7 Sri Lanka 4,576 8 Colombia 4,562 9 Algeria 4,098 10 Somalia 4,090 Since the year 2000, there are 98K records in the dataset. Again, the top 10 are: Country Freq 1 Afghanistan 20,980 2 India 11,409 3 Iraq 6,109 4 Pakistan 5,335 5 Nepal 5,084 6 Somalia 3,664 7 Colombia 3,302 8 Russia  3,115 9 Nigeria 2,901 ...

I have made a video to visualize the variable I created called "airport score". The measurement is created based on global airport network. It shows how centered each city is in the global air traffic network. In short, the airport score for each point on earth (or each city) is the sum product of airport weights and inverse distances to the point from all the airports. The airport weights are obtained through eigenvector centrality using a dataset of all the airline linkages in the world. Method in details 1. There are about 3400 airports in the world, for each point with a longitude and latitude measurement, calculate the distance to each airport: d 2. Apply an inverse function f(x) = 1 / (1 + d)^p , different p gives different result. In the illustration below p = 200 . 2. Time this f(x) with weights w . Then sum over the 3400 airports to get a score. Before the 3D approach, I also tried 2D, which plots the score by horizontal Distance to the center of the city ...