Artículos
Generador de variable aleatoria bivariado aplicado a DEA
Jhon Jairo Vargas-Sánchez- José Adalberto Soto-Mejía
Publicado 2021-02-18
Palabras clave
- análisis envolvente de datos,
- DEA Bayesiano,
- DEA estocástico,
- eficiencias,
- distribución normal multivariada
- generador bivariado,
- sector educativo,
- simulación,
- funciones de densidad de probabilidad,
- programación no lineal,
- conos convexos,
- optimización ...Más
Cómo citar
Vargas-Sánchez, J. J., & Soto-Mejía, J. A. (2021). Generador de variable aleatoria bivariado aplicado a DEA. Revista UIS Ingenierías, 20(2), 139–150. https://doi.org/10.18273/revuin.v20n2-2021012
Resumen
La aplicación de modelos DEA estocásticos utilizando Estadística Bayesiana es una técnica que está surgiendo en los últimos años, para ser usada se debe hacer simulación de distribuciones de probabilidad multivariadas. En este artículo se presenta un generador bivariado para variable continua. Adicionalmente se ha creado una discretización de este para lograr simulaciones de distribuciones a posteriori de una manera fácil de aplicar. Se presentará la aplicación del generador a dos funciones de densidad de probabilidad bivariadas, una de ellas normal, con sus respectivas pruebas de bondad de ajuste. Se usaron datos del sector educativo en base de datos del DANE (Departamento Administrativo Nacional de Estadística) Colombia para resolver el problema de un modelo DEA estocástico Bayesiano. Los resultados muestran la utilidad, potencia y facilidad del uso del generador propuesto en este tipo de problema.
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Referencias
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[7] E. Tsionas, E. Papadakis, “A bayesian approach to statistical inference in stochastic dea”, Omega, vol. 38, no. 5, pp. 309-314, 2010, doi: 10.1016/j.omega.2009.02.003
[8] P. Mitropoulos, M. Talias, I. Mitropoulos, “Combining stochastic dea with bayesian analysis to obtain statistical properties of the efficiency scores: An application to greek public”, Mathematical and Computer Modelling hospitals, vol. 243, no. 1, pp. 302-311, 2015, doi: 10.1016/j.ejor.2014.11.012
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[10] D. Friesner, R. Mittelhammer, R. Rosenman, “Inferring the incidence of industry inefficiency from dea estimates”, European Journal of Operational Research, vol. 224, no, 2, pp. 414-424, 2013, doi: 10.1016/j.ejor.2012.08.003
[11] A. Charnes, W. Cooper, E. Rhodes, “Measuring the efficiency of decision making units”, European Journal of Operation Research, vol. 2, no. 6, pp. 429-444, 1978.
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[14] K. Land, C. Lovell, S. Thore, “Productive e fficiency under capitalism and state socialism: the chance constrained programming approach”, Supplement to Public Finance, vol. 47, pp. 109-121, 1992.
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[16] W. Cooper, L. Seiford, K. Tone, Data envelopment analysis: a comprehensive text with models, aplications, references and DEA-solver software, Second edition. New York, NY, USA: Springer, 2007.
[17] C. Subhash, Data envelopment analysis: theory and techniques for economics and operations research. New York, NY, USA: Cambrige University Press, 2004.
[18] J. Vargas, Simulación Basada en Probabilidad. Manizales: Universidad Autónoma de Manizales, 2013.
[19] S. Korkmaz, D. Goksuluk, G. Zararsiz, “MVN: An r package for assessing multivariate normality”, The R Journal, vol. 6, no. 2, pp. 151-162, 2014.
[20] DANE, “Educación formal educ,” [En línea]. Disponible en: http://www.dane.gov.co/index.php/estadisticas-por-tema/educacion/poblacion-escolarizada/educacion-formal
[21] R. d. C. Ministerio de Educación Nacional, “Educación de calidad,” [En línea]. Disponible en: http://www.mineducacion.gov.co/1621/article-123912.html
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[2] M. Bruni, D. Conforti, P. Beraldi, E. Tundis, “Probabilistically constrained models for efficiency and dominance in dea”, International Journal Production Economics, vol. 117, no. 1, pp. 219-228, 2009, doi: 10.1016/j.ijpe.2008.10.011
[3] L. Simar, P. Wilson, “Sensitivity analysis of efficiency scores: How to bootstrap in nonparametric frontier models”, Management Science., vol. 44, no. 1, pp. 49-61, 1998, doi: 10.1287/mnsc.44.1.49
[4] L. Simar, P. Wilson, “Statistical inference in non-parametric frontier models: the state of the art”, Journal of Productivity Analysis, vol. 13, pp. 49-78, 2000, doi: 10.1023/A:1007864806704
[5] R. Dyson, E. Shale, “Data envelopment analysis, operational research and uncertainty”, Journal of Operational Research Society, vol. 61, pp. 25-34, 2010, doi: 10.1057/jors.2009.145
[6] M. Ceyhan, J. Banneyan, “Handling estimated proportions in public sector data envelopment analysis”, Annals of Operational Research, vol. 221, pp. 107-132, 2014, doi: 10.1007/s10479-011-1007-z
[7] E. Tsionas, E. Papadakis, “A bayesian approach to statistical inference in stochastic dea”, Omega, vol. 38, no. 5, pp. 309-314, 2010, doi: 10.1016/j.omega.2009.02.003
[8] P. Mitropoulos, M. Talias, I. Mitropoulos, “Combining stochastic dea with bayesian analysis to obtain statistical properties of the efficiency scores: An application to greek public”, Mathematical and Computer Modelling hospitals, vol. 243, no. 1, pp. 302-311, 2015, doi: 10.1016/j.ejor.2014.11.012
[9] W. Cooper, Z. Huang, S. Li, “Change constrained DEA”, en Handbook on data envelopment analysis, 2nd ed. Boston: Springer US, 2011, pp. 211-240.
[10] D. Friesner, R. Mittelhammer, R. Rosenman, “Inferring the incidence of industry inefficiency from dea estimates”, European Journal of Operational Research, vol. 224, no, 2, pp. 414-424, 2013, doi: 10.1016/j.ejor.2012.08.003
[11] A. Charnes, W. Cooper, E. Rhodes, “Measuring the efficiency of decision making units”, European Journal of Operation Research, vol. 2, no. 6, pp. 429-444, 1978.
[12] K. Land, C. Lovell, S. Thore, “Productive efficiency under capitalism and state socialism: An empirical inquiry using chance-constrained data envelopment analysis”, Technological Forecasting and Social Change, vol. 46, no. 2, pp. 139-152, 1994, doi: 10.1016/0040-1625(94)90022-1
[13] K. Land, C. Lovell, S. Thore, “Chance-constrained data envelopment analysis”, Managerial and Decision Economics, vol. 14, pp. 541-554, 1993, doi: 10.1002/mde.4090140607
[14] K. Land, C. Lovell, S. Thore, “Productive e fficiency under capitalism and state socialism: the chance constrained programming approach”, Supplement to Public Finance, vol. 47, pp. 109-121, 1992.
[15] K. Land, C. Lovell, S. Thore, “Chance constrained data envelopment analysis”, Managerial and Decision Economics, vol. 14, no. 6, pp. 541-554, 1993, doi: 10.1002/mde.4090140607
[16] W. Cooper, L. Seiford, K. Tone, Data envelopment analysis: a comprehensive text with models, aplications, references and DEA-solver software, Second edition. New York, NY, USA: Springer, 2007.
[17] C. Subhash, Data envelopment analysis: theory and techniques for economics and operations research. New York, NY, USA: Cambrige University Press, 2004.
[18] J. Vargas, Simulación Basada en Probabilidad. Manizales: Universidad Autónoma de Manizales, 2013.
[19] S. Korkmaz, D. Goksuluk, G. Zararsiz, “MVN: An r package for assessing multivariate normality”, The R Journal, vol. 6, no. 2, pp. 151-162, 2014.
[20] DANE, “Educación formal educ,” [En línea]. Disponible en: http://www.dane.gov.co/index.php/estadisticas-por-tema/educacion/poblacion-escolarizada/educacion-formal
[21] R. d. C. Ministerio de Educación Nacional, “Educación de calidad,” [En línea]. Disponible en: http://www.mineducacion.gov.co/1621/article-123912.html
[22] A. Mosek, “The mosek optimization toolbox for matlab manual”, Mosek ApS, Denmark, Tech. Rep. version 7.1, revision 6.0.