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Some properties of the Canberra inequality index

Yıl 2017, Cilt: 46 Sayı: 6, 1159 - 1174, 01.12.2017

Öz

In this paper, we study some properties of the Canberra index which is based on Canberra distance function. Some features that required to an inequality index are investigated. Also we present explicit expression for the Canberra curve in some important inequality distributions. Further, we compare the Canberra curve with the traditional Lorenz curve. A simulation study based on fitted distribution to real income data is performed in order to investigate the asymptotic behavior of the proposed sampling estimator. Finally, the superiority of this index is illustrated by means of a real data set.

Kaynakça

  • Arcagni, A. and Porro, F. The graphical reprensentation of inequality, Revista Colombiana de Estadistica 37 (2), 419-436, 2014.
  • Arnold, B. C. On Zenga and Bonferroni curves, Metron 73 (1), 25-30, 2015.
  • Bonferroni, C. E. Elementi di statistica generale, Università commerciale L. Bocconi, 1961.
  • Cha, S. H. Comprehensive survey on distance measures between probability density function, International Journal of Mathematical Models and Methods in Applied Sciences 4, 343-356, 2007.
  • Chakravarty, S. R. Extended Gini indices of inequality, International Economic Review 29, 147-156, 1988.
  • Gini, C. Variabilita e mutabilita. Reprinted in Memorie di metodologica statistica (Ed. Pizetti E & Salvemini, T), Rome: Libreria Eredi Virgilio Veschi 1, 1912.
  • Hoeffding, W. A class of statistics with asymptotically normal distribution, Journal of Annals of Mathematical Statistics 19, 293-325, 1948.
  • Jedrzejczak, A. Estimation of concentration measures and their standard errors for income distributions in Poland, International Advanced Economic Research 18, 287–297, 2012.
  • Kakwani, N. On a class of poverty measures, Journal of Econometric Society 16, 437-446, 1980.
  • Kleiber, C. and Kotz, S. Statistical Size Distributions in Economics and Actuarial Sciences, John Wiley and Sons, New Jersey, Hoboken, 2003.
  • Lance, G. N. and Williams, W. T. Mixed Data Classificatory Programs I Agglomerative Systems, Statistical size distributions in economics and actuarial sciences 1, 15-20, 1967.
  • Lorenz, M. O. Methods of measuring the concentration of wealth, Journal of the American Statistical Association 9 (70), 209-219, 1905.
  • Mehran, F. Linear measures of income inequality, Journal of Econometric Society 15, 805- 809, 1976.
  • Pietra, G. Delle relazioni fra indici di variabilita note I e II, Atti del Reale Istituto Veneto di Scienze, Lettere ed Arti 74 (2), 775-804, 1915.
  • Polisicchio, M. and Porro, F. A comparison between Lorenz L(p) curve and Zenga I(p) curve, Statistica Applicata 21 (3-4), 289-301, 2009.
  • Sarabia, J. M. Parametric Lorenz curves: models and applications. In Modeling Income Distributions and Lorenz Curves, Springer, New York, 167-190, 2008.
  • Subramanian, S. On a distance function-based inequality measure in the spirit of the Bonferroni and Gini Indices, WIDER Working Paper 62, 2012.
  • Zenga, M. Tendenza alla massima ed alla minima concentrazione per variabili casuali continue, Statistica 44 (4), 619-640, 1984.
  • Zenga, M. Inequality curve and inequality index based on the ratios between lower and upper arithmetic means, Statistica Applicazioni 5 (1), 3-28, 2007.
Yıl 2017, Cilt: 46 Sayı: 6, 1159 - 1174, 01.12.2017

Öz

Kaynakça

  • Arcagni, A. and Porro, F. The graphical reprensentation of inequality, Revista Colombiana de Estadistica 37 (2), 419-436, 2014.
  • Arnold, B. C. On Zenga and Bonferroni curves, Metron 73 (1), 25-30, 2015.
  • Bonferroni, C. E. Elementi di statistica generale, Università commerciale L. Bocconi, 1961.
  • Cha, S. H. Comprehensive survey on distance measures between probability density function, International Journal of Mathematical Models and Methods in Applied Sciences 4, 343-356, 2007.
  • Chakravarty, S. R. Extended Gini indices of inequality, International Economic Review 29, 147-156, 1988.
  • Gini, C. Variabilita e mutabilita. Reprinted in Memorie di metodologica statistica (Ed. Pizetti E & Salvemini, T), Rome: Libreria Eredi Virgilio Veschi 1, 1912.
  • Hoeffding, W. A class of statistics with asymptotically normal distribution, Journal of Annals of Mathematical Statistics 19, 293-325, 1948.
  • Jedrzejczak, A. Estimation of concentration measures and their standard errors for income distributions in Poland, International Advanced Economic Research 18, 287–297, 2012.
  • Kakwani, N. On a class of poverty measures, Journal of Econometric Society 16, 437-446, 1980.
  • Kleiber, C. and Kotz, S. Statistical Size Distributions in Economics and Actuarial Sciences, John Wiley and Sons, New Jersey, Hoboken, 2003.
  • Lance, G. N. and Williams, W. T. Mixed Data Classificatory Programs I Agglomerative Systems, Statistical size distributions in economics and actuarial sciences 1, 15-20, 1967.
  • Lorenz, M. O. Methods of measuring the concentration of wealth, Journal of the American Statistical Association 9 (70), 209-219, 1905.
  • Mehran, F. Linear measures of income inequality, Journal of Econometric Society 15, 805- 809, 1976.
  • Pietra, G. Delle relazioni fra indici di variabilita note I e II, Atti del Reale Istituto Veneto di Scienze, Lettere ed Arti 74 (2), 775-804, 1915.
  • Polisicchio, M. and Porro, F. A comparison between Lorenz L(p) curve and Zenga I(p) curve, Statistica Applicata 21 (3-4), 289-301, 2009.
  • Sarabia, J. M. Parametric Lorenz curves: models and applications. In Modeling Income Distributions and Lorenz Curves, Springer, New York, 167-190, 2008.
  • Subramanian, S. On a distance function-based inequality measure in the spirit of the Bonferroni and Gini Indices, WIDER Working Paper 62, 2012.
  • Zenga, M. Tendenza alla massima ed alla minima concentrazione per variabili casuali continue, Statistica 44 (4), 619-640, 1984.
  • Zenga, M. Inequality curve and inequality index based on the ratios between lower and upper arithmetic means, Statistica Applicazioni 5 (1), 3-28, 2007.
Toplam 19 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm İstatistik
Yazarlar

Shahryar Mirzaei Bu kişi benim

Gholam Reza Mohtashami Borzadaran

Mohammad Amini Bu kişi benim

Hadi Jabbari Bu kişi benim

Yayımlanma Tarihi 1 Aralık 2017
Yayımlandığı Sayı Yıl 2017 Cilt: 46 Sayı: 6

Kaynak Göster

APA Mirzaei, S., Borzadaran, G. R. M., Amini, M., Jabbari, H. (2017). Some properties of the Canberra inequality index. Hacettepe Journal of Mathematics and Statistics, 46(6), 1159-1174.
AMA Mirzaei S, Borzadaran GRM, Amini M, Jabbari H. Some properties of the Canberra inequality index. Hacettepe Journal of Mathematics and Statistics. Aralık 2017;46(6):1159-1174.
Chicago Mirzaei, Shahryar, Gholam Reza Mohtashami Borzadaran, Mohammad Amini, ve Hadi Jabbari. “Some Properties of the Canberra Inequality Index”. Hacettepe Journal of Mathematics and Statistics 46, sy. 6 (Aralık 2017): 1159-74.
EndNote Mirzaei S, Borzadaran GRM, Amini M, Jabbari H (01 Aralık 2017) Some properties of the Canberra inequality index. Hacettepe Journal of Mathematics and Statistics 46 6 1159–1174.
IEEE S. Mirzaei, G. R. M. Borzadaran, M. Amini, ve H. Jabbari, “Some properties of the Canberra inequality index”, Hacettepe Journal of Mathematics and Statistics, c. 46, sy. 6, ss. 1159–1174, 2017.
ISNAD Mirzaei, Shahryar vd. “Some Properties of the Canberra Inequality Index”. Hacettepe Journal of Mathematics and Statistics 46/6 (Aralık 2017), 1159-1174.
JAMA Mirzaei S, Borzadaran GRM, Amini M, Jabbari H. Some properties of the Canberra inequality index. Hacettepe Journal of Mathematics and Statistics. 2017;46:1159–1174.
MLA Mirzaei, Shahryar vd. “Some Properties of the Canberra Inequality Index”. Hacettepe Journal of Mathematics and Statistics, c. 46, sy. 6, 2017, ss. 1159-74.
Vancouver Mirzaei S, Borzadaran GRM, Amini M, Jabbari H. Some properties of the Canberra inequality index. Hacettepe Journal of Mathematics and Statistics. 2017;46(6):1159-74.