Stochastic diffusion process based on Goel–Okumoto curve: statistical inference and application to real data

2022 ◽  
Vol 15 (1) ◽  
pp. 63-71
Author(s):  
Ahmed Nafidi ◽  
Oussama Rida ◽  
Meriem Bahij ◽  
Boujemaa Achchab
Keyword(s):  
Diffusion Process ◽  
Statistical Inference ◽  
Real Data ◽  
Stochastic Diffusion

scholarly journals Stochastic Diffusion Process Based on Generalized Brody Curve: Application to Real Data

2021 ◽  
Vol 2 (1) ◽  
pp. 01-11
Author(s):  
Ahmed Nafidi ◽  
Oussama Rida ◽  
Boujemaa Achchab
Keyword(s):  
Diffusion Process ◽  
Transition Density ◽  
Real Data ◽  
Parameters Estimation ◽  
Likelihood Method ◽  
Stochastic Diffusion ◽  
Life Expectancy At Birth ◽  
Transition Density Function ◽  
Lognormal Diffusion Process ◽  
Trend Functions

A new stochastic diffusion process based on Generalized Brody curve is proposed. Such a process can be considered as an extension of the nonhomogeneous lognormal diffusion process. From the corresponding Itô’s stochastic differential equation (SDE), firstly we establish the probabilistic characteristics of the studied process, such as the solution to the SDE, the probability transition density function and their distribution, the moments function, in particular the conditional and non-conditional trend functions. Secondly, we treat the parameters estimation problem by using the maximum likelihood method in basis of the discrete sampling, thus we obtain nonlinear equations that can be solved by metaheuristic optimization algorithms such as simulated annealing and variable search neighborhood. Finally, we perform a simulation studies and we apply the model to the data of life expectancy at birth in Morocco.

A diffusion process to model generalized von Bertalanffy growth patterns: Fitting to real data

2010 ◽  
Vol 263 (1) ◽  
pp. 59-69 ◽  
Author(s):  
Patricia Román-Román ◽  
Desirée Romero ◽  
Francisco Torres-Ruiz
Keyword(s):  
Diffusion Process ◽  
Real Data ◽  
Growth Patterns ◽  
Von Bertalanffy

scholarly journals An epidemic model for correlated information diffusion in crowd intelligence networks

2019 ◽  
Vol 3 (2) ◽  
pp. 168-183 ◽  
Author(s):  
Yuejiang Li ◽  
H. Vicky Zhao ◽  
Yan Chen
Keyword(s):  
Diffusion Process ◽  
Mixture Model ◽  
Information Diffusion ◽  
Stable State ◽  
Stable Condition ◽  
Real Data ◽  
Information Flows ◽  
Content Type ◽  
Correlated Information ◽  
Crowd Intelligence

Purpose With the popularity of the internet and the increasing numbers of netizens, tremendous information flows are generated daily by the intelligently interconnected individuals. The diffusion processes of different information are not independent, and they interact with and influence each other. Modeling and analyzing the interaction between correlated information play an important role in the understanding of the characteristics of information dissemination and better control of the information flows. This paper aims to model the correlated information diffusion process over the crowd intelligence networks. Design/methodology/approach This study extends the classic epidemic susceptible–infectious–recovered (SIR) model and proposes the SIR mixture model to describe the diffusion process of two correlated pieces of information. The whole crowd is divided into different groups with respect to their forwarding state of the correlated information, and the transition rate between different groups shows the property of each piece of information and the influences between them. Findings The stable state of the SIR mixture model is analyzed through the linearization of the model, and the stable condition can be obtained. Real data are used to validate the SIR mixture model, and the detailed diffusion process of correlated information can be inferred by the analysis of the parameters learned through fitting the real data into the SIR mixture model. Originality/value The proposed SIR mixture model can be used to model the diffusion of correlated information and analyze the propagation process.

Statistical Inference and Simulation with StatKey

2016 ◽  
Vol 109 (9) ◽  
pp. 708-711 ◽  
Author(s):  
Anne Quinn
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Statistical Inference ◽  
Confidence Intervals ◽  
Central Limit ◽  
Real Data ◽  
Web Based ◽  
The Central Limit Theorem

StatKey, a free Web-based app, supplies real data to help with the central limit theorem, confidence intervals, and much more.

A τ-power stochastic gamma diffusion process: Computational statistical inference and simulation aspects. A real example

2012 ◽  
Vol 219 (4) ◽  
pp. 1576-1588
Author(s):  
R. Gutiérrez-Jáimez ◽  
R. Gutiérrez-Sánchez ◽  
A. Nafidi ◽  
E. Ramos-Ábalos
Keyword(s):  
Diffusion Process ◽  
Statistical Inference

scholarly journals Hierarchical Models and Tuning of Random Walk Metropolis Algorithms

2019 ◽  
Vol 2019 ◽  
pp. 1-24 ◽  
Author(s):  
Mylène Bédard
Keyword(s):  
Random Walk ◽  
Diffusion Process ◽  
Hierarchical Models ◽  
Real Data ◽  
Current Position ◽  
Proposal Distribution ◽  
Bayesian Analyses ◽  
Speed Measure ◽  
Random Walk Metropolis ◽  
Random Walk Metropolis Algorithm

We obtain weak convergence and optimal scaling results for the random walk Metropolis algorithm with a Gaussian proposal distribution. The sampler is applied to hierarchical target distributions, which form the building block of many Bayesian analyses. The global asymptotically optimal proposal variance derived may be computed as a function of the specific target distribution considered. We also introduce the concept of locally optimal tunings, i.e., tunings that depend on the current position of the Markov chain. The theorems are proved by studying the generator of the first and second components of the algorithm and verifying their convergence to the generator of a modified RWM algorithm and a diffusion process, respectively. The rate at which the algorithm explores its state space is optimized by studying the speed measure of the limiting diffusion process. We illustrate the theory with two examples. Applications of these results on simulated and real data are also presented.

scholarly journals ASYMMETRIC ANOMALOUS DIFFUSION: AN EFFICIENT WAY TO DETECT MEMORY IN TIME SERIES

Fractals ◽  
2001 ◽  
Vol 09 (04) ◽  
pp. 439-449 ◽  
Author(s):  
PAOLO GRIGOLINI ◽  
LUIGI PALATELLA ◽  
GIACOMO RAFFAELLI
Keyword(s):  
Time Series ◽  
Diffusion Process ◽  
Rare Event ◽  
Real Data ◽  
Scaling Exponent ◽  
Constant Intensity ◽  
Scaling Parameter ◽  
Ballistic Motion ◽  
Maximum Value ◽  
Inverse Power Law

We study time series concerning rare events. The occurrence of a rare event is depicted as a jump of constant intensity always occurring in the same direction, thereby generating an asymmetric diffusion process. We consider the case where the waiting time distribution is an inverse power law with index μ. We focus our attention on μ<3, and we evaluate the scaling exponent δ of the time in the resulting diffusion process. We prove that δ gets its maximum value, δ=1, corresponding to the ballistic motion, at μ=2. We study the resulting diffusion process by means of joint use of the continuous time random walk and of the generalized central limit theorem (CLT), as well as adopting a numerical treatment. We show that rendering the diffusion process to be asymmetric yields the significant benefit of enhancing the value of the scaling parameter δ. Furthermore, this scaling parameter becomes sensitive to the power index μ in the whole region 1<μ<3. Finally, we show our method in action on real data concerning human heartbeat sequences.

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