The Use of Csiszár's Divergence to Assess Dissimilarities of Income Distributions of EU Countries

• Autorzy: Jarosław Oczki , Ewa Wędrowska
• Języki publikacji: EN

Abstrakty

EN

Income distributions can be described by measures of central tendency, dispersion, skewness, kurtosis or by indexes of polarization. In numerous studies, Gini coefficient and Lorenz curve have been used to investigate inequality of incomes. Income distributions can also be analysed in comparison to one another. In the article two measures belonging to Csiszár's divergence class have been used to identify the degree of differentiation of income distributions among the EU countries in 2005 and 2012. Similar and dissimilar countries with respect to distribution of income have been identified and the change of divergence of EU countries income distributions between 2005 and 2012 has been assessed. European Union Statistics on Income and Living Conditions (EU-SILC) dataset has been used. (original abstract)

Słowa kluczowe

EN

Income distribution; Divergence; Research results

PL

Rozkład dochodów; Dywergencja; Wyniki badań

• Czasopismo: Metody Ilościowe w Badaniach Ekonomicznych / Szkoła Główna Gospodarstwa Wiejskiego
• Rocznik: 2014
• Tom: 15(XV)
• Numer: nr 2
• Strony: 167--176

Twórcy

autor

Jarosław Oczki

• Nicolaus Copernicus University in Toruń, Poland

autor

Ewa Wędrowska

• Nicolaus Copernicus University in Toruń, Poland

Bibliografia

• Cavanaugh J. (1999) A Large-Sample Selection Criterion Based on Kullback's Symmetric Divergence, Statistics & Probability Letters, vol. 42, p. 333-343.
• Csiszár I. (1967) Information-Type Measures of Difference of Probability Functions and Indirect Observations, Studia Sci. Math. Hungar, 2, p. 299-318.
• Grosse I., Bernaola-Galva P., Carpena P., Román-Roldan R., Oliver J., Stanley H.E. (2002) Analysis of Symbolic Sequences Using the Jensen-Shannon Divergence, Physical Review E, vol. 65, p. 041905-1 - 041905-16.
• Jędrzejczak A. (2012) Estimation of Concentration Measures and Their Standard Errors for Income Distributions in Poland, International Advances in Economic Research, vol. 18, issue 3, p. 287-297.
• Lamberti P.W., Majtey A.P., Borras A., Casas M., Plastino A. (2008) Metric Character of the Quantum Jensen-Shannon Divergence, Physical Review A, no. 77, p. 052311-1 -052311-6.
• Lefebvre G., Steele R., Vandal A. (2010) A Path Sampling Identity for Computing the Kullback-Leibler and J Divergences. Computational Statistics & Data Analysis, vol. 54, p. 1719 - 1731.
• Menéndez M.L., Pardo J.A., Pardo L., Pardo M.C. (1997) The Jensen-Shannon Divergence, Journal of the Franklin Institute, vol. 134, no. 2, p. 307-318.
• Menéndez M.L., Pardo J.A., Pardo L., Zografos K. (2003) On Tests of Homogeneity Based on Minimum o-divergence Estimator with Constraints, Computational Statistics and Data Analysis, 43, 215-234.
• Podolec B., Ulman P., Wałęga A. (2011) Próba oceny zróżnicowania spożycia artykułów żywnościowych w Polsce na podstawie wyników Badań Budżetów Gospodarstw Domowych, Acta Universitatis Lodziensis, Folia Oeconomica, vol. 253, p. 225-237.
• Quintano C., Castellano R., Regoli A. (2009) Evolution and Decomposition of Income Inequality in Italy, 1991-2004,Statistical Methods and Applications, vol. 18, issue 3, p. 419-443.
• Reid M.D., Williamson R.C. (2009) Generalised Pinsker Inequalities, Proc. of the 22nd Annual Conference on Learning Theory (COLT 2009), Montreal - Quebec.
• Seghouane A.K., Bekara M. (2004) A Small Sample Model Selection Criterion Based on Kullback' s Symmetric Divergence. IEEE Transactions on Signal Processing, vol. 52, p. 3314 - 3323.
• Shannon C.E. (1948) The Mathematical Theory of Communications. Bell Syst. Tech. Journal, vol. 27, p. 423-467.
• Taneja I.J. (2005) Refinement Inequalities Among Symmetric Divergence Measures, The Australian Journal of Mathematical Analysis and Applications, 2 (1), Art. 8, p. 1-23.
• Taneja I.J. (2008) On Mean Divergence Measures, Advances in Inequalities from Probability Theory & Statistics (eds.) N.S. Barnett, S.S. Dragomir, Nova Science Publishers, p. 169-186.
• Taneja I.J. (2013) Generalized Symmetric Divergence Measures and the Probability of Error. Communications in Statistics: Theory & Methods, vol. 42, p. 1654 - 1672.
• Taneja I.J., Kumar P. (2004) Relative Information of Type s, Csiszár's f-Divergence, and Information Inequalities, Information Sciences 166, p. 105-125.
• Tomczyk E. (2011) Application of Measures of Entropy, Information Content and Dissimilarity of Structures to Business Tendency Survey Data, Przegląd Statystyczny, Zeszyt 1-2, p. 88-101.
• Ullah A. (1996) Entropy, Divergence and Distance Measures with Econometric Applications, Journal of Statistical Planning and Inference, 49, p. 137 - 162.
• Wędrowska E. (2011) Application of Kullback-Leibler Relative Entropy for Studies on the Divergence of Household Expenditures Structures, Olsztyn Economic Journal, vol. 6, p. 133-142.
• Wędrowska E. (2012) Miary entropii i dywergencji w analizie struktur, Wyd. Uniwersytetu Warmińsko-Mazurskiego, Olsztyn.