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Comparing TL-Moments, L-Moments and Conventional Moments of Dagum Distribution by Simulated data
Comparación de momentos TL, momentos L y momentos convencionales de la distribución Dagum mediante datos simulados
Keywords:
Dagum distribution, L-moments, Method of moments, Parameter estimation, TL-moments (en)Distribución Dagum, estimacón de parámetros, momentos TL, momentos L, método de momentos (es)
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La modelación de ingresos, salarios, riqueza, gastos y muchas otras variables de tipo social han sido siempre un tema de gran interés. La distribución Dagum es considerada para modelar este tipo de variables. Nos centraremos en este artículo en la derivación de los momentos L y los momentos TL de esta distribución de manera cerrada. Mediante el uso de los estimadores de momentos L y TL, estimamos el parámetro de escala que representa la desigualdad de la distribución de ingresos a partir de la media. Comparando los momentos L, los momentos TL y los momentos convencionales, concluimos que los momentos TL tienen menor sesgo y errores cuadráticos medios. También concluimos que los momentos TL tiene la menor error cuadrático medio para los coeficientes de variación, sesgo y curtosis. Estas conclusiones son igualmente aplicables para todos los tamaños de muestras considerados en nuestro estudio de simulación de Monte Carlo.
1University of Gujrat, Department of Statistics, Gujrat, Pakistan. Professor. Email: nvd.shzd@uog.edu.pk
2Quaid-i-Azam University, Department of Statistics, Islamabad, Pakistan. Doctor. Email: g.zahid@gmail.com
Modeling income, wage, wealth, expenditure and various other social variables have always been an issue of great concern. The Dagum distribution is considered quite handy to model such type of variables. Our focus in this study is to derive the L-moments and TL-moments of this distribution in closed form. Using L & TL-moments estimators we estimate the scale parameter which represents the inequality of the income distribution from the mean income. Comparing L-moments, TL-moments and conventional moments, we observe that the TL-moment estimator has lessbias and root mean square errors than those of L and conventional estimators considered in this study. We also find that the TL-moments have smaller root mean square errors for the coefficients of variation, skewness and kurtosis. These results hold for all sample sizes we have considered in our Monte Carlo simulation study.
Key words: Dagum distribution, L-moments, Method of moments, Parameter estimation, TL-moments.
La modelación de ingresos, salarios, riqueza, gastos y muchas otras variables de tipo social han sido siempre un tema de gran interés. La distribución Dagum es considerada para modelar este tipo de variables. Nos centraremos en este artículo en la derivación de los momentos L y los momentos TL de esta distribución de manera cerrada. Mediante el uso de los estimadores de momentos L y TL, estimamos el parámetro de escala que representa la desigualdad de la distribución de ingresos a partir de la media. Comparando los momentos L, los momentos TL y los momentos convencionales, concluimos que los momentos TL tienen menor sesgo y errores cuadráticos medios. También concluimos que los momentos TL tiene la menor error cuadrático medio para los coeficientes de variación, sesgo y curtosis. Estas conclusiones son igualmente aplicables para todos los tamaños de muestras considerados en nuestro estudio de simulación de Monte Carlo.
Palabras clave: distribución Dagum, estimacón de parámetros, momentos TL, momentos L, método de momentos.
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References
1. Bandourian, R., McDonald, J. & Turley, R. S. (2003), 'A comparison of parametric models of income distribution across countries and over time', Estadistica(55), 135-152.
2. Bílková, D. & Mala, I. (2012), 'Application of the L-moment method when modelling the income distribution in the Czech Republic', Austrian Journal of Statistics 41(2), 125-132.
3. Dagum, C. (1690), A model of Net Wealth Distribution Specified for Negative, Null and Positive Wealth. A Case of Study: Italy, Springer Verlag Berlin, New York.
4. Dagum, C. (1977a), 'The generation and distribution of income, the Lorenz curve and the Gini ratio', Economie Appliquee 33(2), 327-367.
5. Dagum, C. (1977b), 'A new model of personal income distribution: specification and estimation', Economie Appliquee 30(3), 413-437.
6. Dagum, C. & Lemmi, A. (1988), A Contribution to the Analysis of Income Distribution and Income Inequality and a Case Study: Italy, JAI Press, Greenwich.
7. Daud, M. Z., Kassim, A. H. M., Desa, M. N. M. & Nguyen, V. T. V. (2002) Statistical analysis of at-site extreme rainfall processes in peninsular Malaysia 'FRIEND 2002-Regional Hydrology: Bridging the Gap between Research and Practice' number 274 IAHS Publications, Proceedings of International Conferences Cape Town South Africa p. 61-68
8. Elamir, E. A. & Seheult, A. H. (2003), 'Trimmed L-moments', Computational Statistics and Data Analysis(43), 299-314.
9. Hosking, J. R. M. (1990), 'L-moments: analysis and estimation of distributions using linear combinations of order statistics', Journal of the Royal Statistical Society. Series B. Statistical Methodological(52), 105-124.
10. Kleiber, C. (1996), 'Dagum vs. Singh-Maddala income distributions', Economics Letters(53), 265-268.
11. Perez, C. G. & Alaiz, M. P. (2011), 'Using the Dagum model to explain changes in personal income distribution', Applied Economics(43), 4377-4386.
12. Quintano, C. & Dagostino, A. (2006), 'Studying inequality in income distribution of single person households in four developed countries', Review of Income and Wealth(52), 525-546.
13. Shabri, A., Ahmad, N. U. & Zakaria, A. Z. (2011), 'TL-moments and L-moments estimation of the generalized logistic distribution', Journal of Mathematics Research(10), 97-106.
14. Vogel, R. M. & Fennessey, N. M. (1993), 'L-moment diagrams should replace product moment diagrams', Water Resources Research(29), 1745-1752.
15. Ye, Y., Oluyede, B. O. & Pararai, M. (2012), 'Weighted generalized Beta distribution of the second kind and related distributions', Journal of Statistical and Econometric Methods(1), 13-31.
Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:
@ARTICLE{RCEv36n1a05,
AUTHOR = {Shahzad, Mirza Naveed and Asghar, Zahid},
TITLE = {{Comparing TL-Moments, L-Moments and Conventional Moments of Dagum Distribution by Simulated data}},
JOURNAL = {Revista Colombiana de Estadística},
YEAR = {2013},
volume = {36},
number = {1},
pages = {79-93}
}
References
Bandourian, R., McDonald, J. & Turley, R. S. (2003), ‘A comparison of parametric models of income distribution across countries and over time’, Estadistica (55), 135–152.
Bílková, D. & Mala, I. (2012), ‘Application of the L-moment method when modelling the income distribution in the Czech Republic’, Austrian Journal of Statistics 41(2), 125–132.
Dagum, C. (1690), A model of Net Wealth Distribution Specified for Negative, Null and Positive Wealth. A Case of Study: Italy, Springer Verlag Berlin, New York.
Dagum, C. (1977a), ‘The generation and distribution of income, the Lorenz curve and the Gini ratio’, Economie Appliquee 33(2), 327–367.
Dagum, C. (1977b), ‘A new model of personal income distribution: Specification and estimation’, Economie Appliquee 30(3), 413–437.
Dagum, C. & Lemmi, A. (1988), A Contribution to the Analysis of Income Distribution and Income Inequality and a Case Study: Italy, JAI Press, Greenwich.
Daud, M. Z., Kassim, A. H. M., Desa, M. N. M. & Nguyen, V. T. V. (2002), Statistical analysis of at-site extreme rainfall processes in peninsular Malaysia, in H. A. J. van Laanen & S. Demuth, eds, ‘FRIEND 2002-Regional Hydrology: Bridging the Gap between Research and Practice’, number 274, Proceedings of International Conferences, IAHS Publications, Cape Town, South Africa, pp. 61–68.
Elamir, E. A. & Seheult, A. H. (2003), ‘Trimmed L-moments’, Computational Statistics and Data Analysis (43), 299–314.
Hosking, J. R. M. (1990), ‘L-moments: Analysis and estimation of distributions using linear combinations of order statistics’, Journal of the Royal Statistical Society. Series B. Statistical Methodological (52), 105–124.
Kleiber, C. (1996), ‘Dagum vs. Singh-Maddala income distributions’, Economics Letters (53), 265–268.
Perez, C. G. & Alaiz, M. P. (2011), ‘Using the Dagum model to explain changes in personal income distribution’, Applied Economics (43), 4377–4386.
Quintano, C. & Dagostino, A. (2006), ‘Studying inequality in income distribution of single person households in four developed countries’, Review of Income and Wealth (52), 525–546.
Shabri, A., Ahmad, N. U. & Zakaria, A. Z. (2011), ‘TL-moments and L-moments estimation of the generalized logistic distribution’, Journal of Mathematics Research (10), 97–106.
Vogel, R. M. & Fennessey, N. M. (1993), ‘L-moment diagrams should replace product moment diagrams’, Water Resources Research (29), 1745–1752.
Ye, Y., Oluyede, B. O. & Pararai, M. (2012), ‘Weighted generalized Beta distribution of the second kind and related distributions’, Journal of Statistical and Econometric Methods (1), 13–31.
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