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About the modified Gaussian family of income distributions with applications to individual incomes

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  • Sarabia, José María
  • Prieto, Faustino
  • Trueba, Carmen
  • Jordá, Vanesa

Abstract

In a recent paper in this journal [Q. Guo, L. Gao, Distribution of individual incomes in China between 1992 and 2009, Physica A 391 (2012) 5139–5145], a new family of distributions for modeling individual incomes in China was proposed. This family is the so-called Modified Gaussian (MG) distribution, which depends on two parameters. The MG distribution shows a satisfactory fit for the individual income data between 1992 and 2009. However, for the practical use of this model with individual incomes, it is necessary to know its probabilistic and statistical properties, especially the corresponding inequality measures. In this paper, probabilistic functions and inequality measures of the MG distribution are obtained in closed form, including the normalizing constant, probability functions, moments, first-degree stochastic dominance conditions, relationships with other families of distributions and standard tools for inequality measurement (Lorenz and generalized Lorenz curves and Gini, Donaldson–Weymark–Kakwani and Pietra indices). Several methods for parameter estimation are also discussed. In order to illustrate all the previous formulations, we have fitted individual incomes of Spain for three years using the European community household panel survey, concluding a static pattern of inequality, since the Gini index and other inequality measures remain constant over the study period.

Suggested Citation

  • Sarabia, José María & Prieto, Faustino & Trueba, Carmen & Jordá, Vanesa, 2013. "About the modified Gaussian family of income distributions with applications to individual incomes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(6), pages 1398-1408.
    • Handle: RePEc:eee:phsmap:v:392:y:2013:i:6:p:1398-1408
    DOI: 10.1016/j.physa.2012.11.025
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    1. Sarabia, José María & Jordá, Vanesa, 2014. "Explicit expressions of the Pietra index for the generalized function for the size distribution of income," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 416(C), pages 582-595.
    2. Domma, Filippo & Condino, Francesca & Giordano, Sabrina, 2018. "A new formulation of the Dagum distribution in terms of income inequality and poverty measures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 511(C), pages 104-126.
    3. Gao, Li, 2015. "Evolution of consumption distribution and model of wealth distribution in China between 1995 and 2012," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 429(C), pages 76-86.

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