scholarly journals T-Growth Stochastic Model: Simulation and Inference via Metaheuristic Algorithms

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 959
Author(s):  
Antonio Barrera ◽  
Patricia Román-Román ◽  
Francisco Torres-Ruiz
Keyword(s):  
Stochastic Model ◽  
Diffusion Process ◽  
Model Simulation ◽  
Likelihood Estimation ◽  
Real Data ◽  
Estimation Procedure ◽  
Metaheuristic Algorithms ◽  
Mathematical Treatment ◽  
Linear Differential ◽  
Lognormal Diffusion Process

The main objective of this work is to introduce a stochastic model associated with the one described by the T-growth curve, which is in turn a modification of the logistic curve. By conveniently reformulating the T curve, it may be obtained as a solution to a linear differential equation. This greatly simplifies the mathematical treatment of the model and allows a diffusion process to be defined, which is derived from the non-homogeneous lognormal diffusion process, whose mean function is a T curve. This allows the phenomenon under study to be viewed in a dynamic way. In these pages, the distribution of the process is obtained, as are its main characteristics. The maximum likelihood estimation procedure is carried out by optimization via metaheuristic algorithms. Thanks to an exhaustive study of the curve, a strategy is obtained to bound the parametric space, which is a requirement for the application of various swarm-based metaheuristic algorithms. A simulation study is presented to show the validity of the bounding procedure and an example based on real data is provided.

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.

The Odd Log-Logistic Log-Normal Distribution with Theory and Applications

2018 ◽  
Vol 10 (04) ◽  
pp. 1850009 ◽  
Author(s):  
Gamze Ozel ◽  
Emrah Altun ◽  
Morad Alizadeh ◽  
Mahdieh Mozafari
Keyword(s):  
Normal Distribution ◽  
Likelihood Estimation ◽  
Real Data ◽  
Estimation Procedure ◽  
Quantile Function ◽  
Logistic Distribution ◽  
Unknown Parameters ◽  
Heavy Tailed ◽  
Log Normal ◽  
Log Normal Distribution

In this paper, a new heavy-tailed distribution is used to model data with a strong right tail, as often occuring in practical situations. The proposed distribution is derived from the log-normal distribution, by using odd log-logistic distribution. Statistical properties of this distribution, including hazard function, moments, quantile function, and asymptotics, are derived. The unknown parameters are estimated by the maximum likelihood estimation procedure. For different parameter settings and sample sizes, a simulation study is performed and the performance of the new distribution is compared to beta log-normal. The new lifetime model can be very useful and its superiority is illustrated by means of two real data sets.

scholarly journals Stochastic Brennan–Schwartz Diffusion Process: Statistical Computation and Application

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1062 ◽  
Author(s):  
Ahmed Nafidi ◽  
Ghizlane Moutabir ◽  
Ramón Gutiérrez-Sánchez
Keyword(s):  
Diffusion Process ◽  
Real Data ◽  
Convertible Bond ◽  
Financial Mathematics ◽  
Continuous Sampling ◽  
Statistical Computation ◽  
Likelihood Approach ◽  
Lognormal Diffusion Process ◽  
Trend Functions ◽  
The One

In this paper, we study the one-dimensional homogeneous stochastic Brennan–Schwartz diffusion process. This model is a generalization of the homogeneous lognormal diffusion process. What is more, it is used in various contexts of financial mathematics, for example in deriving a numerical model for convertible bond prices. In this work, we obtain the probabilistic characteristics of the process such as the analytical expression, the trend functions (conditional and non-conditional), and the stationary distribution of the model. We also establish a methodology for the estimation of the parameters in the process: First, we estimate the drift parameters by the maximum likelihood approach, with continuous sampling. Then, we estimate the diffusion coefficient by a numerical approximation. Finally, to evaluate the capability of this process for modeling real data, we applied the stochastic Brennan–Schwartz diffusion process to study the evolution of electricity net consumption in Morocco.

scholarly journals The Exponentiated Burr XII Power Series Distribution: Properties and Applications

Stats ◽  
2018 ◽  
Vol 2 (1) ◽  
pp. 15-31
Author(s):  
Arslan Nasir ◽  
Haitham Yousof ◽  
Farrukh Jamal ◽  
Mustafa Korkmaz
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Power Series ◽  
Likelihood Estimation ◽  
Real Data ◽  
Estimation Procedure ◽  
Model Parameters ◽  
Data Sets ◽  
Power Series Distributions ◽  
New Distribution

In this work, we introduce a new Burr XII power series class of distributions, which is obtained by compounding exponentiated Burr XII and power series distributions and has a strong physical motivation. The new distribution contains several important lifetime models. We derive explicit expressions for the ordinary and incomplete moments and generating functions. We discuss the maximum likelihood estimation of the model parameters. The maximum likelihood estimation procedure is presented. We assess the performance of the maximum likelihood estimators in terms of biases, standard deviations, and mean square of errors by means of two simulation studies. The usefulness of the new model is illustrated by means of three real data sets. The new proposed models provide consistently better fits than other competitive models for these data sets.

scholarly journals A STOCHASTIC MODEL FOR THE COOPERATIVE RELAXATION OF PROTEINS, BASED ON A HIERARCHY OF INTERACTIONS BETWEEN AMINO ACIDIC RESIDUES

1998 ◽  
Vol 08 (02) ◽  
pp. 327-358 ◽  
Author(s):  
M. ABUNDO ◽  
L. ACCARDI ◽  
L. STELLA ◽  
N. ROSATO
Keyword(s):  
Molecular Dynamics ◽  
Amino Acids ◽  
Stochastic Model ◽  
Diffusion Process ◽  
Discrete System ◽  
Real Data ◽  
The Other ◽  
Hierarchic Structure ◽  
Protein Molecules ◽  
Cooperative Relaxation

In this paper, a stochastic model for the cooperative relaxation of proteins, based on a hierarchic structure of the interactions between amino acids is proposed. It relies on the arbitrary splitting of interactions into two classes, strong and weak, and tests the preponderance of one class over the other. The presented model generalizes a first one valid for homogeneous interactions in the protein molecules previously studied by the authors. The time evolution of the system is studied as a function of five parameters, three of which are related to the cooperativity. Moreover, different approximations of the discrete system to a diffusion process, and to a Poisson process are considered, according to the magnitude of the parameters. A method for estimating the parameters from real data is proposed. Finally, numerical simulations and a comparison with the molecular dynamics of a real protein (Barnase) are reported.

scholarly journals The Stochastic Modified Lundqvist-Korf Diffusion Process: Statistical and Computational Aspects and Application to Modeling of the CO2 Emission in Morocco

2021 ◽  
Author(s):  
Ahmed Nafidi ◽  
Abdenbi El azri ◽  
Ramón Gutiérrez Sanchez
Keyword(s):  
Diffusion Process ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Real Data ◽  
Trend Function ◽  
Non Linear Equation ◽  
New Process ◽  
Computational Aspects ◽  
Exogenous Factors ◽  
Trend Functions

Abstract The main goal of this paper is to study the possibility of using a stochastic non-homogeneous (without exogenous factors) diffusion process to model the evolution of CO2 emissions in Morocco and concretely using a new process, in which the trend function is proportional to the modified Lundqvist-Korf growth curve. First, the main characteristics of the process are studied, then we establish a computational statistical methodology based on the maximum likelihood estimation method and the trend functions. When we are estimating the parameters of the process, a non-linear equation is obtained and the simulated annealing method is proposed to solve it after bounding the parametric space by a stagewise procedure. Also, to validate this methodology, we include the results obtained from several examples of simulation. Finally, the process and the methodology established are applied to real data corresponding to the evolution of CO2 emissions in Morocco.

scholarly journals The beta-burr type v distribution: its properties and application to real life data

2017 ◽  
Vol 5 (2) ◽  
pp. 83
Author(s):  
Hussaini Garba Dikko ◽  
Yakubu Aliyu ◽  
Saidu Alfa
Keyword(s):  
Real Life ◽  
Real Data ◽  
Estimation Procedure ◽  
Cumulative Distribution ◽  
Mathematical Treatment ◽  
Data Set ◽  
Life Data ◽  
Real Life Data ◽  
Type V ◽  
New Distribution

A new distribution called the beta-Burr type V distribution that extends the Burr type V distribution was defined, investigated and estab-lished. The properties examined provide a comprehensive mathematical treatment of the distribution. Additionally, various structural proper-ties of the new distribution verified include probability density function verification, asymptotic behavior, Hazard Rate Function and the cumulative distribution. Subsequently, we used the maximum likelihood estimation procedure to estimate the parameters of the new distribu-tion. Application of real data set indicates that this new distribution would serve as a good alternative distribution function to model real- life data in many areas.

scholarly journals General Purpose MRF Learning with Neural Network Potentials

2020 ◽  
Author(s):  
Hao Xiong ◽  
Nicholas Ruozzi
Keyword(s):  
Maximum Likelihood ◽  
Markov Random Fields ◽  
Likelihood Estimation ◽  
Real Data ◽  
Estimation Procedure ◽  
General Purpose ◽  
Data Sets ◽  
Continuous Variables ◽  
Generative Modeling ◽  
Learning Frameworks

Maximum likelihood learning is a well-studied approach for fitting discrete Markov random fields (MRFs) to data. However, general purpose maximum likelihood estimation for fitting MRFs with continuous variables have only been studied in much more limited settings. In this work, we propose a generic MLE estimation procedure for MRFs whose potential functions are modeled by neural networks. To make learning effective in practice, we show how to leverage a highly parallelizable variational inference method that can easily fit into popular machining learning frameworks like TensorFlow. We demonstrate experimentally that our approach is capable of effectively modeling the data distributions of a variety of real data sets and that it can compete effectively with other common methods on multilabel classification and generative modeling tasks.

scholarly journals Curves Classification by Using a Local Likelihood Function and Its Practical Usefulness for Real Data

2020 ◽  
Author(s):  
Mustapha Rachdi ◽  
Ali Laksaci ◽  
Ali Hamié ◽  
Jacques Demongeot ◽  
Idir Ouassou
Keyword(s):  
Likelihood Function ◽  
Kernel Estimation ◽  
Likelihood Estimation ◽  
Real Data ◽  
Estimation Procedure ◽  
Error Rates ◽  
Gaussian Kernel ◽  
Local Likelihood ◽  
Classification Error ◽  
Linear Predictors

We extend the classical approach in supervised classification based on the local likelihood estimation to the functional covariates case. The estimation procedure of the functional parameter (slope parameter) in the linear model when the covariate is of functional kind is investigated. We show, on simulated as well on real data, that classification error rates estimated using test samples, and the estimation procedure by local likelihood seem to lead to better estimators than the classical kernel estimation. In addition, this approach is no longer assuming that the linear predictors have a specific parametric form. However, this approach also has two drawbacks. Indeed, it was more expensive and slower than the kernel regression. Thus, as mentioned earlier, kernels other than the Gaussian kernel can lead to a divergence of the Newton-Raphson algorithm. In contrast, using a Gaussian kernel, 4 to 6 iterations are then sufficient to achieve convergence.

THE DEVELOPMENT OF THE MATHEMATICAL MODEL OF PREDICTING THE INDICATORS OF ACCREDITATION OF TECHNICAL UNIVERSITIES IN THE RUSSIAN FEDERATION

2017 ◽  
pp. 27-38
Author(s):  
Olga Mikhaylovna Tikhonova ◽  
Alexander Fedorovich Rezchikov ◽  
Vladimir Andreevich Ivashchenko ◽  
Vadim Alekseevich Kushnikov
Keyword(s):  
Mathematical Model ◽  
System Dynamics ◽  
Regression Model ◽  
Oriented Graph ◽  
Real Data ◽  
Educational Process ◽  
Proposed Model ◽  
Linear Differential ◽  
The University ◽  
The Mathematical Model

The paper presents the system of predicting the indicators of accreditation of technical universities based on J. Forrester mechanism of system dynamics. According to analysis of cause-and-effect relationships between selected variables of the system (indicators of accreditation of the university) there was built the oriented graph. The complex of mathematical models developed to control the quality of training engineers in Russian higher educational institutions is based on this graph. The article presents an algorithm for constructing a model using one of the simulated variables as an example. The model is a system of non-linear differential equations, the modelling characteristics of the educational process being determined according to the solution of this system. The proposed algorithm for calculating these indicators is based on the system dynamics model and the regression model. The mathematical model is constructed on the basis of the model of system dynamics, which is further tested for compliance with real data using the regression model. The regression model is built on the available statistical data accumulated during the period of the university's work. The proposed approach is aimed at solving complex problems of managing the educational process in universities. The structure of the proposed model repeats the structure of cause-effect relationships in the system, and also provides the person responsible for managing quality control with the ability to quickly and adequately assess the performance of the system.

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