Abstract:

       Power law behaviors are ubiquitous in natural and social phenomena. How to accurately describe such behaviors and provide reasonable explanations of why such behaviors occur, however, has long been a standing open problem. The double Pareto lognormal distribution offers, from the stochastic process point of view, a viable approach to this problem. This article elaborates the mathematical concept of the double Pareto lognormal distribution and provides an overview of natural and social phenomena that exhibit such distribution. These include the number of friends in social networks, Internet file sizes, stock market returns, wealth possessions in human societies, human settlement sizes, oil field reserves, and areas burnt from forest wildfire.

Key words: double Pareto lognormal distribution, complex network, natural and social phenomena