Is there a universal parametric city size distribution? Empirical evidence for 70 countries

Abstract

We study the parametric description of the city size distribution (CSD) of 70 different countries (developed and developing) using seven models, as follows: the lognormal (LN), the loglogistic (LL), the double Pareto lognormal (dPLN), the two-lognormal (2LN), the two-loglogistic (2LL), the three-lognormal (3LN) and the three-loglogistic (3LL). Our results show that 3LN and 3LL are the best densities in terms of non-rejections out of stan-Financial support from Ministerio de Economía y Competitividad (ECO2017-82246-P) and support by Aragon Government (ADETRE Consolidated Group) is acknowledged.

Log-growth rates of CO2: An empirical analysis

“…On the contrary, we find a great variability, depending on the years considered, regarding the best density. This outcome is in line with the key message derived from [38,39]. This reflects the effort made by most countries in the reduction of CO 2 emissions, with some countries with a higher effort than others, leading to year-to-year shifts in the statistical distribution of CO 2 emissions among nations.…”

“…where erf denotes the error function associated to the standard normal distribution. The 2-mixture of normal distributions (2N), is [20,21,22,28,38,39,7]…”

“…In this paper we perform the first attempt, to the best of our knowledge, to define the densities that fit best to the observed data. The distributions chosen are the exponentiated versions of that in [2], that is to say, the normal (N), the asymmetric double Laplace normal (adLN) (exponentiated version of the double Pareto lognormal, dPLN), the exponential tails normal (ETN) (exponentiated version of the Pareto tails lognormal, PTLN) 2 and the exponentiated version of two densities recently introduced in the literature of city sizes and strike size [28,6,22,21,48,38,39,7], namely a mixture of two (2N) or three (3N) normal distributions (see also, e.g., [35]).…”

How sensitive is city size distribution to the definition of city? The case of Spain

“…For municipalities the chosen function is the three-lognormal (3LN), for the cities defined in Arribas-Bel et al (2019) the chosen function is the double Pareto-lognormal (dPLN), for AUDES ( Áreas Urbanas de España) data the best density is the Pareto one and for FUA OECD (Functional Urban Areas) data the outperforming function is the truncated lognormal; in each case, the selected distributions are never rejected according to the information in Table 1. This result is related to the main conclusion derived from Puente-Ajovín et al (2020), that is to say, different countries are best described (in terms of information criteria) by different densities and not by a single dominating one, although there maybe densities that are not rejected (almost) always by standard statistical tests.…”

The Probability Distribution of Worldwide Forest Areas

“…This kind of convoluted distributions could provide a more accurate fit to the probability distribution of forest areas. To date, they have only been applied to study city size distributions [65][66][67][68] and the size distribution of national CO 2 emissions [16].…”