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Research Article

Graphical representations and associated goodness-of-fit tests for Pareto and log-normal distributions based on inequality curves

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Pages 464-481 | Received 27 May 2020, Accepted 29 Aug 2021, Published online: 18 Sep 2021

References

  • Afhami, B., and Madadi, M. (2017), ‘Entropy-based Goodness-of-fit Tests for the Pareto I Distribution’, Communications in Statistics – Theory and Methods, 46(8), 3649–3666.
  • Arcagni, A., and Porro, F. (2016), ‘A Comparison of Income Distributions Models Throught Inequality Curves’, Statistica & Applicazioni, XIV(2), 123–144.
  • Cirillo, P. (2013), ‘Are Your Data Really Pareto Distributed?’, Physica A: Statistical Mechanics and its Applications, 392(23), 5947–5962.
  • Clauset, A.N., Shalizi, C.R., and Newman, M.E.J. (2009), ‘Power-law Distributions in Empirical Data’, SIAM Review, 51(4), 661–703.
  • D'Agostino, R.B., and Stephens, M.A. (eds.) (1986), Goodness-of-fit-techniques, New York, NY: Marcel Dekker.
  • Dey, A.K., and Kundu, D. (2009), ‘Discriminating Between the Log-normal and Log-logistic Distributions’, Communications in Statistics – Theory and Methods, 39(2), 280–292.
  • Eeckhout, J. (2004), ‘Gibrat's Law for (all) Cities’, American Economic Review, 94(5), 1429–1451.
  • Eeckhout, J. (2009), ‘Gibrat's Law for (all) Cities: Reply’, American Economic Review, 99(4), 1676–1683.
  • Gabaix, X., and Ioannides, Y.M. (2004), ‘The Evolution of City Size Distributions’, Handbook of Regional and Urban Economics, 4, 2341–2378.
  • Goldie, C.M. (1977), ‘Convergence Theorems for Empirical Lorenz Curves and Their Inverses’, Advances in Applied Probability, 9(4), 765–791.
  • Grahovac, D., Jia, M., Leonenko, N.N., and Taufer, E. (2015), ‘Asymptotic Properties of the Partition Function and Applications in Tail Index Inference of Heavy-tailed Data’, Statistics: A Journal of Theoretical and Applied Statistics, 49, 1221–1242.
  • Heyde, C.C., and Kou, S.G. (2004), ‘On the Controversy Over Tailweight of Distributions’, Operations Research Letters, 32(5), 399–408.
  • Jammalamadaka, S.R., and Goria, M.N. (2004), ‘A Test of Goodness-of-fit Based on Gini's Index of Spacings’, Statistics & Probability Letters, 68(2), 177–187.
  • Jammalamadaka, S.R., and Tian, G. (2018), ‘Indirect Inference for Fitting Income Distributions’, Journal of the Indian Society for Probability and Statistics, 19(2), 345–358.
  • Jia, M., Taufer, E., and Dickson, M. (2018), ‘Semi-parametric Regression Estimation of the Tail Index’, Electronic Journal of Statistics, 12, 224–248.
  • Kratz, M.F., and Resnick, S.I. (1996), ‘The QQ-estimator and Heavy Tails’, Communications in Statistics. Stochastic Models, 12(4), 699–724.
  • Kundu, D., Gupta, R.D., and Manglick, A. (2005), ‘Discriminating Between the Log-normal and Generalized Exponential Distributions’, Journal of Statistical Planning and Inference, 127(1–2), 213–227.
  • Levy, M. (2009), ‘Gibrat's Law for (all) Cities: Comment’, American Economic Review, 99(4), 1672–1675.
  • Lloyd, C.J. (2005), ‘Estimating Test Power Adjusted for Size’, Journal of Statistical Computation and Simulation, 75(11), 921–933.
  • Meintanis, S.G. (2008), ‘A Powerful Method of Assessing the Fit of the Lognormal Distribution’, Communications in Statistics – Theory and Methods, 37(11–12), 1948–1958.
  • Meintanis, S.G. (2009), ‘A Unified Approach of Testing for Discrete and Continuous Pareto Laws’, Statistical Papers, 50(3), 569–580.
  • Obradović, M., Jovanović, M., and Milošević, B. (2015), ‘Goodness-of-fit Tests for Pareto Distribution Based on a Characterization and Their Asymptotics’, Statistics, 49(5), 1026–1041.
  • Raqab, M.Z., Al-Awadhi, S.A., and Kundu, D. (2018), ‘Discriminating Among Weibull, Log-normal, and Log-logistic Distributions’, Communications in Statistics – Simulation and Computation, 47(5), 1397–1419.
  • Rizzo, M.L. (2009), ‘New Goodness-of-fit Tests for Pareto Distributions’, ASTIN Bulletin: The Journal of the IAA, 39(2), 691–715.
  • Taufer, E., Santi, F., Novi Inverardi, P.L., Espa, G., and Dickson, M.M. (2020), ‘Extreme Value Index Estimation by Means of An Inequality Curve’, Mathematics, 8, 1834.
  • Volkova, K. (2016), ‘Goodness-of-fit Tests for the Pareto Distribution Based on Its Characterization’, Statistical Methods & Applications, 25(3), 351–373.
  • Zenga, M. (1984), ‘Proposta Per Un Indice Di Concentrazione Basato Sui Rapporti Fra Quantili Di Popolazione E Quantili Di Reddito’, Giornale degli Economisti e Annali di Economia, 5/6, 301–326.
  • Zenga, M. (1990), ‘Concentration Curves and Concentration Indexes Derived From Them’, in Income and Wealth Distribution, Inequality and Poverty, eds. C. Dagum and M. Zenga, Springher -Verlag, pp. 94–110.
  • Zenga, M. (2007), ‘Inequality Curve and Inequality Index Based on the Ratios Between Lower and Upper Arithmetic Means’, Statistica e Applicazioni, 1, 3–27.

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