×

Characterization of distributions by properties of truncated Gini index and mean difference. (English) Zbl 1302.62025

Summary: The right truncated Gini index and mean difference are useful tools in the analysis of incomes and the left truncated versions of these functions can be employed in reliability modelling. In this paper we identify the distributions characterized by simple functional forms of these measures and also by relationships they have with poverty measures and reliability functions. Finally, we provide an application of proposed results in modelling statistical data.

MSC:

62E10 Characterization and structure theory of statistical distributions
62N05 Reliability and life testing
62P20 Applications of statistics to economics
91B82 Statistical methods; economic indices and measures

Software:

LMOMENTS
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Borroni, C.G. and Zenga, M. (2007) A test of concordance based on Gini’s mean difference, Statistical Methods and Applications, 16, 289–308. · Zbl 1405.62067
[2] Eliazar, I.I. and Sokolov, I.M. (2010) Connection between Gini index and extreme value statistic, Physics A.: Statistical Mechanics and Applications, 389, 4462–2274.
[3] Farris, F.A. (2010) Gini index and measures of inequality, American Mathematical Monthly, 117, 851–864. · Zbl 1203.91224
[4] Harch, B.D., Correl, R.L., Meech, W., Kirkby, C.A. and Pankhurst, C.E. (1997) Using the Gini coefficient with BIOLOG substrate unitisation data to provide alternative quantitative measures for comparing bacterial soil communities, Journal of Microbiological Methods, 30, 91–101.
[5] Haritha, N.H., Nair, N.U. and Nair, K.R.M. (2008) Modelling incomes using generalised lambda distributions, Journal of Income Distributions, 17, 37–51.
[6] Hosking, J.R.M. (1990) L-moments: analysis and estimation of distribution using linear combination of order statistics, Journal of the Royal Statistical Society, B 52, 105–124. · Zbl 0703.62018
[7] Kleiber, C. Kotz, S. (2003) Statistical Size Distributions in Economics and Actuarial Sciences, Wiley Interscience. · Zbl 1044.62014
[8] Lai, C. D. and Xie, M. (2006) Stochastic Ageing and Dependence for Reliability, Springer. · Zbl 1098.62130
[9] Liao, Y. (2010) The concentration ratio of China construction industry market, International Conference on Management and Service Science, MASS 2010, Article No. 5577404.
[10] Nair, N.U. and Sankaran, P.G. (2009) Quantile based reliability analysis, Communications in Statistics-Theory and Methods, 38, 222–232. · Zbl 1292.62025
[11] Nair, N.U. and Vineshkumar, B. (2010) L-moments of residual life, Journal of Statistical Planning and Inference, 140, 2618–2631. · Zbl 1188.62293
[12] Pereira, G.M., Feitas, M.A.V. and Da Silva, N.F. (2011) The challenge of energy poverty: Brazilian case study, Energy Policy, 39, 167–175.
[13] Sadras, V.O. and Bongiovanni, R. (2004) Use of Lorenz curves and Gini coefficients to assess yield inequality within paddocks, Field Crops Research, 90, 303–310.
[14] Sen, A. (1976) Poverty: an ordinal approach to measurement, Econometrica, 44, 219–231. · Zbl 0349.90017
[15] Tarsitano, A. (2004) Fitting generalized lambda distribution to income data, In: ’COMPSTAT 2004 Symposium’, Springer, pp. 1861–1867.
[16] Yitzhaki, S. (2003) Gini’s mean difference: a superior measure of variability for non normal distributions, Metron, LXI, 285–316.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.