Decompositions by sources and by subpopulations of the Pietra index: two applications to professional football teams in Italy

In this paper two innovative procedures for the decomposition of the Pietra index are proposed. The first one allows the decomposition by sources, while the second one provides the decomposition by subpopulations. As special case of the latter procedure, the “classical” decomposition in two components (within and between) can be easily obtained. A remarkable feature of both the proposed procedures is that they permit the assessment of the contribution to the Pietra index at the smallest possible level: each source for the first one and each subpopulation for the second one. To highlight the usefulness of these procedures, two applications are provided regarding Italian professional football (soccer) teams.

[1]  D. Wilkinson,et al.  Increasingly inequitable distribution of general practitioners in Australia, 1986–96 , 2001, Australian and New Zealand journal of public health.

[2]  B. Starfield,et al.  The relationship between primary care, income inequality, and mortality in US States, 1980-1995. , 2003, The Journal of the American Board of Family Practice.

[3]  J. Vlachý,et al.  Identifying a set of inequality measures for science studies , 1978, Scientometrics.

[4]  C. Lionis,et al.  Measuring health inequalities in Albania: a focus on the distribution of general practitioners , 2006, Human resources for health.

[5]  J. Sarabia,et al.  Explicit expressions of the Pietra index for the generalized function for the size distribution of income , 2014 .

[6]  I. Kawachi,et al.  Social capital, income inequality, and firearm violent crime. , 1998, Social science & medicine.

[7]  B. Khanal.  IS COMMUNITY FORESTRY DECREASING THE INEQUALITY AMONG ITS USERS? STUDY ON IMPACT OF COMMUNITY FORESTRY ON INCOME DISTRIBUTION AMONG DIFFERENT USERS GROUPS IN NEPAL , 2011 .

[8]  F. Porro,et al.  The Gini Coefficient and the Case of Negative Values , 2019 .

[9]  P. Muliere,et al.  A note on inequality measures and the Pigou-Dalton principle of transfers , 1990 .

[10]  L. Hirschhorn,et al.  Estimating health workforce needs for antiretroviral therapy in resource-limited settings , 2006, Human resources for health.

[11]  Ichiro Kawachi,et al.  Income distribution and mortality: cross sectional ecological study of the Robin Hood index in the United States , 1996, BMJ.

[12]  C. Chen,et al.  Inequalities in neighborhood child asthma admission rates and underlying community characteristics in one US county. , 2013, The Journal of pediatrics.

[13]  A. Manero,et al.  The limitations of negative incomes in the Gini coefficient decomposition by source , 2017 .

[14]  R. Khalilnejad,et al.  Equality in Distribution of Human Resources: the Case of Iran’s Ministry of Health and Medical Education , 2013, Iranian journal of public health.

[15]  C. Dagum.  A new approach to the decomposition of the Gini income inequality ratio , 1997 .

[16]  M. O. Lorenz,et al.  Methods of Measuring the Concentration of Wealth , 1905, Publications of the American Statistical Association.

[17]  Samuel M. Otterstrom,et al.  Spatial Patterns of Migration and Income Change in the Mountain West: The Dominance of Service-Based, Amenity-Rich Counties , 2001 .

[18]  H. Alker,et al.  On measuring inequality. , 1964, Behavioral science.

[19]  Fernando De Maio,et al.  Income inequality measures , 2007 .

[20]  Y. Leung,et al.  Measuring Regional Inequality: A Comparison of Coefficient of Variation and Hoover Concentration Index , 2009 .

[21]  Approximation and decomposition of Gini, Pietra–Ricci and Theil inequality measures , 2012 .

[22]  On unbiased estimation of gini index and yntema-pietra index of lognormal distribution and their variances , 1989 .

[23]  Ričardas Zitikis,et al.  An index of monotonicity and its estimation: a step beyond econometric applications of the Gini index , 2005 .

[24]  C. Dagum.  A new approach to the decomposition of the Gini income inequality ratio , 1997 .

[25]  E. van Doorslaer,et al.  On the interpretation of a concentration index of inequality. , 2004, Health economics.

[26]  M. Zenga,et al.  Components of Gini, Bonferroni, and Zenga Inequality Indexes for EU Income Data , 2018 .

[27]  A. Shorrocks,et al.  Inequality Decomposition by Population Subgroups , 1984 .

[28]  Igor M. Sokolov,et al.  Measuring statistical heterogeneity: The Pietra index , 2010 .

[29]  G. M. Borzadaran,et al.  Entropy maximization under the constraints on the generalized Gini index and its application in modeling income distributions , 2015 .

[30]  D. Wilkinson,et al.  Inequitable distribution of general practitioners in Australia: estimating need through the Robin Hood Index , 2000, Australian and New Zealand journal of public health.

[31]  A. Shorrocks,et al.  Inequality Decompositions By Factor Components , 1982 .

[32]  J. Ray,et al.  Measuring the Concentration of Power in the International System , 1973 .

[33]  Frank A. Cowell,et al.  Measurement of income inequality: Experimental test by questionnaire , 1992 .

[34]  Edgar M. Hoover,et al.  The Measurement of Industrial Localization , 1936 .

[35]  José María Sarabia,et al.  Parametric Lorenz Curves: Models and Applications , 2008 .

[36]  P. Rogerson,et al.  The Hoover Index of Population Concentration and the Demographic Components of Change , 2013 .

[37]  Tahir Ekin,et al.  Topic modelling for medical prescription fraud and abuse detection , 2018, Journal of the Royal Statistical Society: Series C (Applied Statistics).