Mathematical Modeling of Consumer Behavior, Taking into Account Entropy

Ermilov, Mikhail M.; Surkova, Liudmila E.; Samoletov, Roman V.

doi:10.1007/978-3-030-57831-2_28

“…Employment rate, for example, is known to be strongly related to aggregate measures of consumer spending [29,30] especially during times of crisis. Our analysis sheds light on the role of entropy measures of human mobility in economic analyses, contributing to the literature of mathematical modeling of consumer behaviors in relation to mobility regularities [31][32][33]. We provide an epidemiological model for the effective reproduction number in combination with entropy-based metrics of human mobility and we reveal relationships between economic indicators and mobility-based variables, underscoring how economic activity and human movement are intertwined.…”

Section: Introductionmentioning

confidence: 74%

On an Aggregated Estimate for Human Mobility Regularities through Movement Trends and Population Density

Vanni,

Lambert

2024

Preprint

0

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This article introduces an analytical framework that interprets individual measures of entropy-based mobility derived from mobile phone data. We explore and analyze two widely recognized entropy metrics: random entropy and uncorrelated Shannon entropy. These metrics are estimated through collective variables of human mobility, including movement trends and population density. By employing a collisional model, we establish statistical relationships between entropy measures and mobility variables. Furthermore, our research addresses three primary objectives: firstly, validating the model; secondly, exploring correlations between aggregated mobility and entropy measures in comparison to five economic indicators; and finally, demonstrating the utility of entropy measures. Specifically, we provide an effective population density estimate that offers a more realistic understanding of social interactions. This estimation takes into account both movement regularities and intensity, utilizing real-time data analysis conducted during the peak period of the Covid-19 pandemic.

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“…Our analysis sheds light on the role of entropy measures of human mobility in economic analyses, contributing to the literature on the mathematical modeling of consumer behaviors in relation to mobility regularities [43][44][45]. We provide an epidemiological model for the effective reproduction number in combination with entropy-based metrics of human mobility and we reveal relationships between economic indicators and mobility-based variables, underscoring how economic activity and human movement are intertwined.…”

Section: Introductionmentioning

confidence: 74%

On an Aggregated Estimate for Human Mobility Regularities through Movement Trends and Population Density

Vanni,

Lambert

2024

Entropy

0

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This article introduces an analytical framework that interprets individual measures of entropy-based mobility derived from mobile phone data. We explore and analyze two widely recognized entropy metrics: random entropy and uncorrelated Shannon entropy. These metrics are estimated through collective variables of human mobility, including movement trends and population density. By employing a collisional model, we establish statistical relationships between entropy measures and mobility variables. Furthermore, our research addresses three primary objectives: firstly, validating the model; secondly, exploring correlations between aggregated mobility and entropy measures in comparison to five economic indicators; and finally, demonstrating the utility of entropy measures. Specifically, we provide an effective population density estimate that offers a more realistic understanding of social interactions. This estimation takes into account both movement regularities and intensity, utilizing real-time data analysis conducted during the peak period of the COVID-19 pandemic.

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“…All linear and a lot of essentially nonlinear models of mathematical physics are homogeneous (symmetric) in some sense. Homogeneous models can be utilized as local approximations of dynamical systems if, for example, linearisation is too conservative, noninformative, or simply impossible" [7, p. vii] Homogeneity has been applied in several areas such as: image processing [29], classification [13], [30], control [7], economy [31], [32] and others. It is not difficult to see its broad application, since every linear function is homogeneous.…”

Section: Introductionmentioning

confidence: 99%

Abstract Homogeneous Functions and Consistently Influenced/Disturbed Multi-Expert Decision Making

Santiago

¹

,

Bedregal

²

,

Dimuro

³

et al. 2022

IEEE Trans. Fuzzy Syst.

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In this paper we propose a new generalization for the notion of homogeneous functions. We show some properties and how it appears in some scenarios. Finally we show how this generalization can be used in order to provide a new paradigm for decision making theory called consistent influenced/disturbed decision making. In order to illustrate the applicability of this new paradigm, we provide a toy example.

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Mathematical Modeling of Consumer Behavior, Taking into Account Entropy

Cited by 5 publications

References 6 publications

On an Aggregated Estimate for Human Mobility Regularities through Movement Trends and Population Density

On an Aggregated Estimate for Human Mobility Regularities through Movement Trends and Population Density

On an Aggregated Estimate for Human Mobility Regularities through Movement Trends and Population Density

Abstract Homogeneous Functions and Consistently Influenced/Disturbed Multi-Expert Decision Making

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