This study provides a systematic review of the existing literature on Zipf's law for city size
distribution. Existing empirical evidence suggests that Zipf's law is not always observable …

We review stochastic processes without detailed balance condition and derive their H-
theorem. We obtain stationary distributions and investigate their stability in terms of …

We test the validity of Zipf's and Gibrat's laws for city size distributions at the regional level
from 1900 to 2010 by considering US states. Zipf's law is satisfied for a majority of states, but …

This paper examines the Zipf's law for the size distribution of Pakistani cities using the five
census data from 1951 to 1998. We observe that Zipf's law does not hold in any of the five …

We apply five distributions–lognormal, double-Pareto lognormal, lognormal-upper tail
Pareto, Pareto tails-lognormal, and Pareto tails-lognormal with differentiability restrictions–to …

Income distribution models can be useful for describing the economic properties of a
population. In this study, three-part composite Pareto models are fitted to the income …

We study the parametric distribution of log-growth rates of CO 2 and CO 2 per capita
emissions for 207 countries and territories taking data from 1994 to 2010. We define the log …

We present a statistical model with 8 parameters that combines three components, namely a
truncated lognormal distribution central body with a lower and an upper tail, both consisting …

The widely recognized rank-size law is being questioned as the single best rule for city size
distribution by an increasing number of studies. However, these studies suffer from …

The Pareto distribution is widely applied in many areas of studies such as economics and
sciences. An important issues related to Pareto tail modelling is to determine the optimal …