A Note on Estimation of Multi-Sigmoidal Gompertz Functions with Random Noise

Román-Román, Patricia; Serrano-Pérez, Juan José; Torres-Ruiz, Francisco

doi:10.3390/math7060541

Cited by 16 publications

(17 citation statements)

References 26 publications

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“…Regarding oscillabolastic process X L (t), given by SDE (9), the maximum likelihood estimation can be addressed by means of the procedure described in [6]. This approach has already been used succesfully in the inferential treatment of the Gompertz multisigmoidal diffusion process [7], as well as in the generalization of the classic Weibull model, in particular for the hyperbolastic type III diffusion process [19].…”

Section: Lognormal Casementioning

confidence: 99%

“…In this sense it is worth highlighting the role of the lognormal process with exogenous factors. As a matter of fact, concrete choices of such exogenous factors lead to processes by which we may study patterns of behavior modeled by a wide range of growth curves (see Román-Román et al [6,7] and references therein). These references are related to the one-dimensional case, although there are extensions to multidimensionality such as the one proposed by Rupšys in [8], where a 4-variate Bertalanffy-type SDE is considered.…”

Section: Introductionmentioning

confidence: 99%

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Two Stochastic Differential Equations for Modeling Oscillabolastic-Type Behavior

2020

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Stochastic models based on deterministic ones play an important role in the description of growth phenomena. In particular, models showing oscillatory behavior are suitable for modeling phenomena in several application areas, among which the field of biomedicine stands out. The oscillabolastic growth curve is an example of such oscillatory models. In this work, two stochastic models based on diffusion processes related to the oscillabolastic curve are proposed. Each of them is the solution of a stochastic differential equation obtained by modifying, in a different way, the original ordinary differential equation giving rise to the curve. After obtaining the distributions of the processes, the problem of estimating the parameters is analyzed by means of the maximum likelihood method. Due to the parametric structure of the processes, the resulting systems of equations are quite complex and require numerical methods for their resolution. The problem of obtaining initial solutions is addressed and a strategy is established for this purpose. Finally, a simulation study is carried out.

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Section: Lognormal Casementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Two Stochastic Differential Equations for Modeling Oscillabolastic-Type Behavior

2020

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“…In this regard, we can cite the work of Fernandes et al ( 2017 ) who modeled the growth of coffee berries by double sigmoid function. In addition, Román-Román et al ( 2019 ) proposed multi-sigmoidal Gompertz functions to describe growth at multiple inflection points.…”

Section: Introductionmentioning

confidence: 99%

Mathematical model of Boltzmann’s sigmoidal equation applicable to the spreading of the coronavirus (Covid-19) waves

Aferni¹,

Guettari²,

Tajouri³

2020

Environ Sci Pollut Res

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Currently, investigations are intensively conducted on modeling, forecasting, and studying the dynamic spread of coronavirus (Covid-19) new pandemic. In the present work, the sigmoidal-Boltzmann mathematical model was applied to study the Covid-19 spread in 15 different countries. The cumulative number of infected persons I has been accurately fitted by the sigmoidal-Boltzmann equation (SBE), giving rise to different epidemiological parameters such as the pandemic peak t p , the maximum number of infected persons I max , and the time of the epidemic stabilization t ∞. The time constant relative to the sigmoid Δt (called also the slope factor) was revealed to be the determining parameter which influences all the epidemiological parameters. Empirical laws between the different parameters allowed us to propose a modified sigmoidal-Boltzmann equation describing the spread of the pandemic. The expression of the spread speed V p was further determined as a function of the sigmoid parameters. This made it possible to assess the maximum speed of spread of the virus V pmax and to trace the speed profile in each country. In addition, for countries undergoing a second pandemic wave, the cumulative number of infected people I has been successfully adjusted by a double sigmoidal-Boltzmann equation (DSBE) allowing the comparison between the two waves. Finally, the comparison between the maximum virus spread of two waves V p max 1 and V p max 2 showed that the intensity of the second wave of Covid-19 is low compared to the first for all the countries studied.

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“…Tree size variables can be modeled as a complex system, each with its own regulatory mechanism and all continuously interacting between them. The mathematical and numerical methods used to describe the dynamic of biological system are largely concerned with the derivation, and use of ordinary stochastic and partial differential equations [3,4]. Individual-tree and stand-level growth models traditionally are represented by a system of ordinary differential equations [5].…”

Section: Introductionmentioning

confidence: 99%

Understanding the Evolution of Tree Size Diversity within the Multivariate Nonsymmetrical Diffusion Process and Information Measures

Rupšys

2019

Mathematics

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This study focuses on the stochastic differential calculus of Itô, as an effective tool for the analysis of noise in forest growth and yield modeling. Idea of modeling state (tree size) variable in terms of univariate stochastic differential equation is exposed to a multivariate stochastic differential equation. The new developed multivariate probability density function and its marginal univariate, bivariate and trivariate distributions, and conditional univariate, bivariate and trivariate probability density functions can be applied for the modeling of tree size variables and various stand attributes such as the mean diameter, height, crown base height, crown width, volume, basal area, slenderness ratio, increments, and much more. This study introduces generalized multivariate interaction information measures based on the differential entropy to capture multivariate dependencies between state variables. The present study experimentally confirms the effectiveness of using multivariate interaction information measures to reconstruct multivariate relationships of state variables using measurements obtained from a real-world data set.

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A Note on Estimation of Multi-Sigmoidal Gompertz Functions with Random Noise

Cited by 16 publications

References 26 publications

Two Stochastic Differential Equations for Modeling Oscillabolastic-Type Behavior

Two Stochastic Differential Equations for Modeling Oscillabolastic-Type Behavior

Mathematical model of Boltzmann’s sigmoidal equation applicable to the spreading of the coronavirus (Covid-19) waves

Understanding the Evolution of Tree Size Diversity within the Multivariate Nonsymmetrical Diffusion Process and Information Measures

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