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Comparisons of log-normal mixture and Pareto tails, GB2 or log-normal body of Romania’s all cities size distribution

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  • Băncescu, Irina
  • Chivu, Luminiţa
  • Preda, Vasile
  • Puente-Ajovín, Miguel
  • Ramos, Arturo

Abstract

Modeling demographic data has been on the agenda of statisticians for many years. Some of the distributions used are Pareto, reverse Pareto, q-exponential and log-normal models. An approach to this problem is to consider three statistical models: one for the upper tail, one for the middle range, and another for the lower tail. This paper deals with the size distribution of urban and rural agglomerations in Romania for the 1992–2017 period, by comparing the recently introduced three log-normal mixture (3LN), Pareto tails log-normal (PTLN), and threshold double Pareto Generalized Beta of second kind (tdPGB2) models. The tdPGB2 statistical model has the PTLN distribution as a limiting case. The maximum likelihood estimates of the distributions are computed, and goodness-of-fit tests are performed using the Kolmogorov–Smirnov (KS), Cramér–von Mises (CM) and Anderson–Darling (AD) statistics. Also, we use the Vuong and Bayes factor log-likelihood tests. Using both graphical and formal statistical tests, our results rigorously confirm that the 3LN model is statistically equivalent to PTLN and tdPGB2 distributions, the preferred model being the PTLN probability law. Both the PTLN and tdPGB2 distributions have Pareto tails but the 3LN model does not. All the three models prove to be very well suited parameterizations of Romania’s city size data.

Suggested Citation

  • Băncescu, Irina & Chivu, Luminiţa & Preda, Vasile & Puente-Ajovín, Miguel & Ramos, Arturo, 2019. "Comparisons of log-normal mixture and Pareto tails, GB2 or log-normal body of Romania’s all cities size distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 526(C).
    • Handle: RePEc:eee:phsmap:v:526:y:2019:i:c:s0378437119306272
    DOI: 10.1016/j.physa.2019.04.253
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    Citations

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    Cited by:

    1. Peña, Guillermo & Puente-Ajovín, Miguel & Ramos, Arturo & Sanz-Gracia, Fernando, 2022. "Log-growth rates of CO2: An empirical analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 588(C).
    2. Băncescu, Irina & Chivu, Luminiţa & Massing, Till & Preda, Vasile & Puente-Ajovín, Miguel & Ramos, Arturo, 2024. "On the parametric description of log-growth rates of Romanian city sizes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 643(C).
    3. Tomaschitz, Roman, 2020. "Multiply broken power-law densities as survival functions: An alternative to Pareto and lognormal fits," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 541(C).
    4. Campolieti, Michele & Ramos, Arturo, 2021. "The distribution of strike size: Empirical evidence from Europe and North America in the 19th and 20th centuries," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 563(C).
    5. Milićević Snežana & Petrović Jelena & Đorđević Nataša, 2020. "ICT as a factor of destination competitiveness: The case of the republics of former Yugoslavia," Management & Marketing, Sciendo, vol. 15(3), pages 381-392, September.
    6. Catana, Luigi-Ionut, 2022. "Stochastic orders of multivariate Jones–Larsen distribution family with empirical applications in physics, economy and social sciences," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 603(C).

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