The population sizes of the cities in the world follow the same distribution in the past 30 years

-
This week has been busy. Since yesterday I have been working on the paper discussing the population size data of all the cities in the world. There are some very interesting findings and I can write several posts about it.

One interesting finding is that contrary to some prevalent imagination that there are more and more large cities and the small cities are diminishing, our findings based on the population data of all the cities in the world since the year 1990 indicate such statement is wrong. More large cities do not necessarily imply fewer small cities. Thus, when there are more large cities, there are also more small cities proportionally. And since the total number of cities with size above 100 thousand is increasing, the share of small or large cities in the world remains the same.


Comments

Post a Comment

Popular posts from this blog

How to Draw Heatmap with Colorful Dendrogram

-
Image
Heatmap with Dendrogram: Color Branches and Labels This data visualization example include: * Hierarchical clustering, dendrogram, and heat map based on normalized odds ratios * The dendrogram was built separately to give color to dendrogram’s branches/labels based on clusters using  dendextend * Heatmap is made by  heatmap.2  from  gplots  using the built dendrogram * The rows are sorted by means from highest to lowest, it can be done in either the dendrogram or the  heatmap.2 * Use color palettes from  colorspace Data YRBSS (Youth Risk Behavior Surveillance System) survey data from CDC. This example plots the odds ratios of 63 behavioral questions on one question regarding disordered eating. The odds ratios are median centered by column and log2 transformed Version 1: Color both the branches and labels library (curl) # read file from google drive library (gplots) # heatmap.2 library (dendextend) # make and color dendrogram library (colorspace) #
Read more

Power-law distribution (Pareto)& Zipf's Law: connection and how to fit the distribution of global city population

-
Image
- 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 follow a hig
Read more

eXtreme Gradient Boosting (XGBoost): Better than random forest or gradient boosting

-
Image
Ensemble Methods 1. Random Forest 2. Gradient boosting 3. Extreme Gradient Boosting Compared to Lasso and Best-subset Lasso Best-subset Compare MSEs Code I recently had the great pleasure to meet with Professor Allan Just and he introduced me to eXtreme Gradient Boosting (XGBoost). XGBoost is “one of the most loved machine learning algorithms at Kaggle”, it somehow combines the advantages of random forest and boosting. We will see later its predictive ability is indeed very strong. In the earlier post  Model Selection using Lasso and Best Subset  I mainly focused on model selection by best-subset, stepwise, or lasso. This post will focus on ensemble method: random forest, Gradient boosting, and eXtreme Gradient Boosting (XGBoost). An ensemble method is a technique that combines the predictions from multiple machine learning algorithms together to make more accurate predictions than any individual model. 1. Random Forest Use library  randomForest . A
Read more