Modeling the Dynamics of the Frequent Users of Electronic Commerce in Spain Using Optimization Techniques for Inverse Problems with Uncertainty

Clara Burgos (), Juan-Carlos Cortés (), Iván-Camilo Lombana (), David Martínez-Rodríguez () and Rafael-J. Villanueva ()
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Clara Burgos: Universitat Politècnica de València
Juan-Carlos Cortés: Universitat Politècnica de València
Iván-Camilo Lombana: Universidad Cooperativa de Colombia
David Martínez-Rodríguez: Universitat Politècnica de València
Rafael-J. Villanueva: Universitat Politècnica de València

Journal of Optimization Theory and Applications, 2019, vol. 182, issue 2, No 15, 785-796

Abstract: Abstract 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.

Keywords: Inverse problem; Uncertainty quantification; Random optimization computational methods; Nonlinear stochastic model; Probability density function; 65C20; 65C60; 65K10 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10957-018-1382-6

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