Modeling the Dynamics of the Frequent Users of Electronic Commerce in Spain Using Optimization Techniques for Inverse Problems with Uncertainty
In this paper, we retrieve data about the frequent users of electronic commerce during the period 2011–2016 from the Spanish National Institute of Statistics. These data, coming from surveys, have intrinsic uncertainty that we describe using appropriate random variables. Then, we propose a stochasti...
- Autores:
-
Burgos, Clara
Cortés, Juan Carlos
Lombana, Iván Camilo
Martínez Rodríguez, David
Villanueva, Rafael Jacinto
- Tipo de recurso:
- Article of journal
- Fecha de publicación:
- 2020
- Institución:
- Universidad Cooperativa de Colombia
- Repositorio:
- Repositorio UCC
- Idioma:
- OAI Identifier:
- oai:repository.ucc.edu.co:20.500.12494/28358
- Acceso en línea:
- https://doi.org/10.1007/s10957-018-1382-6
https://hdl.handle.net/20.500.12494/28358
- Palabra clave:
- Inverse problem
Uncertainty quantification
Random optimization computational methods
Nonlinear stochastic model
Probability density function
- Rights
- closedAccess
- License
- Atribución
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Modeling the Dynamics of the Frequent Users of Electronic Commerce in Spain Using Optimization Techniques for Inverse Problems with Uncertainty |
| title |
Modeling the Dynamics of the Frequent Users of Electronic Commerce in Spain Using Optimization Techniques for Inverse Problems with Uncertainty |
| spellingShingle |
Modeling the Dynamics of the Frequent Users of Electronic Commerce in Spain Using Optimization Techniques for Inverse Problems with Uncertainty Inverse problem Uncertainty quantification Random optimization computational methods Nonlinear stochastic model Probability density function |
| title_short |
Modeling the Dynamics of the Frequent Users of Electronic Commerce in Spain Using Optimization Techniques for Inverse Problems with Uncertainty |
| title_full |
Modeling the Dynamics of the Frequent Users of Electronic Commerce in Spain Using Optimization Techniques for Inverse Problems with Uncertainty |
| title_fullStr |
Modeling the Dynamics of the Frequent Users of Electronic Commerce in Spain Using Optimization Techniques for Inverse Problems with Uncertainty |
| title_full_unstemmed |
Modeling the Dynamics of the Frequent Users of Electronic Commerce in Spain Using Optimization Techniques for Inverse Problems with Uncertainty |
| title_sort |
Modeling the Dynamics of the Frequent Users of Electronic Commerce in Spain Using Optimization Techniques for Inverse Problems with Uncertainty |
| dc.creator.fl_str_mv |
Burgos, Clara Cortés, Juan Carlos Lombana, Iván Camilo Martínez Rodríguez, David Villanueva, Rafael Jacinto |
| dc.contributor.author.none.fl_str_mv |
Burgos, Clara Cortés, Juan Carlos Lombana, Iván Camilo Martínez Rodríguez, David Villanueva, Rafael Jacinto |
| dc.subject.other.spa.fl_str_mv |
Inverse problem Uncertainty quantification Random optimization computational methods Nonlinear stochastic model Probability density function |
| topic |
Inverse problem Uncertainty quantification Random optimization computational methods Nonlinear stochastic model Probability density function |
| description |
In this paper, we retrieve data about the frequent users of electronic commerce during the period 2011–2016 from the Spanish National Institute of Statistics. These data, coming from surveys, have intrinsic uncertainty that we describe using appropriate random variables. Then, we propose a stochastic model to study the dynamics of frequent users of electronic commerce. The goal of this paper is to solve the inverse problem that consists of determining the model parameters as suitable parametric random variables, in such a way the model output be capable of capturing the data uncertainty, at the time instants where sample data are available, via adequate probability density functions. To achieve the aforementioned goal, we propose a computational procedure that involves building a nonlinear objective function, based on statistical moment measures, to be minimized using a variation of the particle swarm optimization algorithm. |
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2020-12-02T21:56:40Z 2026-12-02 |
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2020-12-02 |
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Artículo |
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Lombana, I. C., Burgos, C., Cortés J. C., Villanueva R. J. y Martínez D. (2019). Modeling the Dynamics of the Frequent Users of Electronic Commerce in Spain Using Optimization Techniques for Inverse Problems with Uncertainty. Journal of Optimization Theory and Applications, (182), 785-796. https://doi.org/10.1007/s10957-018-1382-6 |
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0022-3239 Lombana, I. C., Burgos, C., Cortés J. C., Villanueva R. J. y Martínez D. (2019). Modeling the Dynamics of the Frequent Users of Electronic Commerce in Spain Using Optimization Techniques for Inverse Problems with Uncertainty. Journal of Optimization Theory and Applications, (182), 785-796. https://doi.org/10.1007/s10957-018-1382-6 |
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https://doi.org/10.1007/s10957-018-1382-6 https://hdl.handle.net/20.500.12494/28358 |
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Journal of Optimization Theory and Applications |
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Dorini, F.A., Cecconello, M.S., Dorini, M.B.: On the logistic equation subject to uncertainties in the environmental carrying capacity and initial population density. Commun. Nonlinear Sci. Numer. Simul. 33, 160–173 (2016). https://doi.org/10.1016/j.cnsns.2015.09.009 Hussein, A., Selim, M.M.: Solution of the stochastic radiative transfer equation with Rayleigh scattering using RVT technique. Appl. Math. Comput. 218(13), 7193–7203 (2012). https://doi.org/10.1016/j.amc.2011.12.088 Dorini, F., Cunha, M.: Statistical moments of the random linear transport equation. J. Comput. Phys. 227(19), 8541–8550 (2008). https://doi.org/10.1016/j.jcp.2008.06.002 Xu, Z., Tipireddy, R., Lin, G.: Analytical approximation and numerical studies of one-dimensional elliptic equation with random coefficients. Appl. Math. Model. 40(9–10), 5542–5559 (2016). https://doi.org/10.1016/j.apm.2015.12.04 Mourad, K., Debbouche, A.: Complete controllability of nonlocal fractional stochastic differential evolution equations with Poisson jumps in Hilbert spaces. Int. J. Adv. Appl. Math. Mech. 3(1), 41–48 (2015) Casabán, M.C., Cortés, J.C., Navarro-Quiles, A., Romero, J.V., Roselló, M.D., Villanueva, R.J.: A comprehensive probabilistic solution of random SIS-type epidemiological models using the random variable transformation technique. Commun. Nonlinear Sci. Numer. Simul. 32, 199–210 (2016). https://doi.org/10.1016/j.cnsns.2015.08.009 Casabán, M.C., Cortés, J.C., Navarro-Quiles, A., Romero, J.V., Roselló, M.D., Villanueva, R.J.: Computing probabilistic solutions of the Bernoulli random differential equation. J. Comput. Appl. Math. 309, 396–407 (2017). https://doi.org/10.1016//j.cam.2016.02.034 Cortés, J.C., Santonja, F.J., Tarazona, A.C., Villanueva, R.J., Villanueva-Oller, J.: A probabilistic estimation and prediction technique for dynamic continuous social science models: the evolution of the attitude of the basque country population towards ETA as a case study. Appl. Math. Comput. 264, 13–20 (2015). https://doi.org/10.1016/j.amc.2015.03.128 Spanish INE: Encuesta sobre equipamiento y uso de tecnologías de información y comunicación en los hogares (Survey on equipment and use of the information technologies and communication in the household. http://www.ine.es/dyngs/INEbase/es/operacion.htm?c=Estadistica_C&cid=1254736176741&menu=resultados&idp=1254735576692. Accessed 20 June 2018 Spanish INE: Indicadores demográficos básicos (Basic demographic indicators). http://www.ine.es/dyngs/INEbase/es/operacion.htm?c=Estadistica_C&cid=1254736177003&menu=resultados&idp=1254735573002. Accessed 20 June 2018 Christakis, N.A., Fowler, J.H.: Connected: The Surprising Power of Our Social Networks and How They Shape Our Lives. Little, Brown and Company, Boston (2009) Brauer, F., Castillo-Chávez, C.: Mathematical Models in Population Biology and Epidemiology. Springer, New York (2001). https://doi.org/10.1007/978-1-4757-3516-1 Norman, L., Kotz, S., Balakrishnan, N.: Continuous Univariate Distributions. Wiley, London (1994) Khemka, N., Jacob, C.: Exploratory toolkit for evolutionary and swarm-based optimization. Math. J. 11(3), 376–391 (2010). https://doi.org/10.3888/tmj.11.3-5 Acedo, L., Burgos, C., Hidalgo, J.I., Sánchez-Alonso, V., Villanueva, R.J., Villanueva-Oller, J.: Calibrating a large network model describing the transmission dynamics of the human papillomavirus using a particle swarm optimization algorithm in a distributed computing environment. Int. J. High Perf. Comput. Appl. (2017). https://doi.org/10.1177/1094342017697862 |
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Burgos, ClaraCortés, Juan CarlosLombana, Iván CamiloMartínez Rodríguez, DavidVillanueva, Rafael Jacinto1822020-12-02T21:56:40Z2020-12-02T21:56:40Z2026-12-022020-12-020022-3239https://doi.org/10.1007/s10957-018-1382-6https://hdl.handle.net/20.500.12494/28358Lombana, I. C., Burgos, C., Cortés J. C., Villanueva R. J. y Martínez D. (2019). Modeling the Dynamics of the Frequent Users of Electronic Commerce in Spain Using Optimization Techniques for Inverse Problems with Uncertainty. Journal of Optimization Theory and Applications, (182), 785-796. https://doi.org/10.1007/s10957-018-1382-6In this paper, we retrieve data about the frequent users of electronic commerce during the period 2011–2016 from the Spanish National Institute of Statistics. These data, coming from surveys, have intrinsic uncertainty that we describe using appropriate random variables. Then, we propose a stochastic model to study the dynamics of frequent users of electronic commerce. The goal of this paper is to solve the inverse problem that consists of determining the model parameters as suitable parametric random variables, in such a way the model output be capable of capturing the data uncertainty, at the time instants where sample data are available, via adequate probability density functions. To achieve the aforementioned goal, we propose a computational procedure that involves building a nonlinear objective function, based on statistical moment measures, to be minimized using a variation of the particle swarm optimization algorithm.https://scienti.minciencias.gov.co/cvlac/visualizador/generarCurriculoCv.do?cod_rh=0001220268http://orcid.org/0000-0002-6528-2155https://scienti.minciencias.gov.co/gruplac/jsp/visualiza/visualizagr.jsp?nro=00000000002516clabursi@gmail.comjccortes@mat.upv.esivan.lombana@campusucc.edu.codamarro3@upv.esrjvillan@imm.upv.es785-796Universidad Cooperativa de Colombia, Facultad de Ingenierías, Ingeniería Civil, IbaguéIngeniería CivilIbaguéInverse problemUncertainty quantificationRandom optimization computational methodsNonlinear stochastic modelProbability density functionModeling the Dynamics of the Frequent Users of Electronic Commerce in Spain Using Optimization Techniques for Inverse Problems with UncertaintyArtículohttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1http://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionAtribucióninfo:eu-repo/semantics/closedAccesshttp://purl.org/coar/access_right/c_14cbJournal of Optimization Theory and ApplicationsDorini, F.A., Cecconello, M.S., Dorini, M.B.: On the logistic equation subject to uncertainties in the environmental carrying capacity and initial population density. Commun. Nonlinear Sci. Numer. Simul. 33, 160–173 (2016). https://doi.org/10.1016/j.cnsns.2015.09.009Hussein, A., Selim, M.M.: Solution of the stochastic radiative transfer equation with Rayleigh scattering using RVT technique. Appl. Math. Comput. 218(13), 7193–7203 (2012). https://doi.org/10.1016/j.amc.2011.12.088Dorini, F., Cunha, M.: Statistical moments of the random linear transport equation. J. Comput. Phys. 227(19), 8541–8550 (2008). https://doi.org/10.1016/j.jcp.2008.06.002Xu, Z., Tipireddy, R., Lin, G.: Analytical approximation and numerical studies of one-dimensional elliptic equation with random coefficients. Appl. Math. Model. 40(9–10), 5542–5559 (2016). https://doi.org/10.1016/j.apm.2015.12.04Mourad, K., Debbouche, A.: Complete controllability of nonlocal fractional stochastic differential evolution equations with Poisson jumps in Hilbert spaces. Int. J. Adv. Appl. Math. Mech. 3(1), 41–48 (2015)Casabán, M.C., Cortés, J.C., Navarro-Quiles, A., Romero, J.V., Roselló, M.D., Villanueva, R.J.: A comprehensive probabilistic solution of random SIS-type epidemiological models using the random variable transformation technique. Commun. Nonlinear Sci. Numer. Simul. 32, 199–210 (2016). https://doi.org/10.1016/j.cnsns.2015.08.009Casabán, M.C., Cortés, J.C., Navarro-Quiles, A., Romero, J.V., Roselló, M.D., Villanueva, R.J.: Computing probabilistic solutions of the Bernoulli random differential equation. J. Comput. Appl. Math. 309, 396–407 (2017). https://doi.org/10.1016//j.cam.2016.02.034Cortés, J.C., Santonja, F.J., Tarazona, A.C., Villanueva, R.J., Villanueva-Oller, J.: A probabilistic estimation and prediction technique for dynamic continuous social science models: the evolution of the attitude of the basque country population towards ETA as a case study. Appl. Math. Comput. 264, 13–20 (2015). https://doi.org/10.1016/j.amc.2015.03.128Spanish INE: Encuesta sobre equipamiento y uso de tecnologías de información y comunicación en los hogares (Survey on equipment and use of the information technologies and communication in the household. http://www.ine.es/dyngs/INEbase/es/operacion.htm?c=Estadistica_C&cid=1254736176741&menu=resultados&idp=1254735576692. Accessed 20 June 2018Spanish INE: Indicadores demográficos básicos (Basic demographic indicators). http://www.ine.es/dyngs/INEbase/es/operacion.htm?c=Estadistica_C&cid=1254736177003&menu=resultados&idp=1254735573002. Accessed 20 June 2018Christakis, N.A., Fowler, J.H.: Connected: The Surprising Power of Our Social Networks and How They Shape Our Lives. Little, Brown and Company, Boston (2009)Brauer, F., Castillo-Chávez, C.: Mathematical Models in Population Biology and Epidemiology. Springer, New York (2001). https://doi.org/10.1007/978-1-4757-3516-1Norman, L., Kotz, S., Balakrishnan, N.: Continuous Univariate Distributions. Wiley, London (1994)Khemka, N., Jacob, C.: Exploratory toolkit for evolutionary and swarm-based optimization. Math. J. 11(3), 376–391 (2010). https://doi.org/10.3888/tmj.11.3-5Acedo, L., Burgos, C., Hidalgo, J.I., Sánchez-Alonso, V., Villanueva, R.J., Villanueva-Oller, J.: Calibrating a large network model describing the transmission dynamics of the human papillomavirus using a particle swarm optimization algorithm in a distributed computing environment. Int. J. High Perf. Comput. Appl. 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