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323694

Enhancing Reliability and Accuracy in Stochastic Growth Modeling: Method of Three Selected Points Approach

Article

Last updated: 05 Jan 2025

Subjects

-

Tags

Applied Mathematics

Abstract

Growth models play a pivotal role in diverse fields, such as population dynamics, epidemiology, finance, and ecological systems. Traditionally, deterministic growth models have been extensively employed to capture various aspects of growth phenomena. However, in real-world scenarios, stochasticity is inherent in the data, challenging the suitability of deterministic models. Consequently, there is a growing interest in developing stochastic growth models capable of accommodating inherent uncertainties. This study addresses three fundamental questions within the context of stochastic growth modeling. Firstly, it investigates the continued reliability of the  Method of Three Selected Points (MTSP) for estimating parameters in stochastic differential equations (SDEs), given the increasing popularity of stochastic models over deterministic ones. Secondly, it explores the required form of SDEs that maximizes the success and reliability of the MTSP approach. Lastly, it conducts a comparative analysis of the MTSP method against commonly employed techniques in the literature. 
    To address these questions, we propose a novel approach to constructing SDEs that enhance the stability of both bounded and unbounded stochastic growth models. By carefully selecting the form of the diffusion coefficient, we achieve higher accuracy in estimating the parameters of the drift coefficient. Through empirical simulations and a comprehensive reliability analysis using real stock data, we demonstrate the superior performance of the MTSP method when compared to the Pseudo-maximum likelihood method and physics-informed neural networks within the framework of SDEs. Our findings underscore the continued effectiveness of the MTSP method for estimating parameters in stochastic growth models, even in an era where stochastic models dominate. Additionally, we provide insights into the optimal structure of SDEs for maximizing the reliability of the MTSP approach. Thus, the study contributes to the ongoing dialogue surrounding stochastic growth modeling and offers a robust methodology for parameter estimation in this context, with practical applications in fields ranging from epidemiology to finance.

DOI

10.21608/cjmss.2023.240689.1021

Keywords

Method of Three Selected Points,  Reliability analysis,  Logistic curve,  Stochastic Differential Equations

Authors

First Name

Patrick

Last Name

Chidzalo

MiddleName

-

Affiliation

Department of Applied Studies, Malawi Institute of Technology, Malawi University of Science and Technology, Limbe, Malawi

Email

pchidzalo@must.ac.mw

City

-

Orcid

0000-0003-3958-1415

First Name

John

Last Name

Abonongo

MiddleName

-

Affiliation

School of Mathematical Sciences, Department of Statistics and Actuarial Science, C. K. Tedam University of Technology and Applied Sciences, Navrongo, Ghana

Email

abonongojohn@gmail.com

City

Juja

Orcid

0000-0003-2149-7709

First Name

Raphael

Last Name

Naryongo

MiddleName

-

Affiliation

School of Engineering and Technology, Department of Electronics and Computer Engineering, Soroti University, Arapai, Uganda

Email

rnaryongo@sun.ac.ug

City

Arapai

Orcid

0000-0003-3671-0752

Volume

2

Article Issue

2

Related Issue

40924

Issue Date

2023-11-01

Receive Date

2023-10-04

Publish Date

2023-11-01

Page Start

291

Page End

302

Print ISSN

2974-3435

Online ISSN

2974-3443

Link

https://cjmss.journals.ekb.eg/article_323694.html

Detail API

https://cjmss.journals.ekb.eg/service?article_code=323694

Order

323,694

Type

Original Article

Type Code

2,545

Publication Type

Journal

Publication Title

Computational Journal of Mathematical and Statistical Sciences

Publication Link

https://cjmss.journals.ekb.eg/

MainTitle

Enhancing Reliability and Accuracy in Stochastic Growth Modeling: Method of Three Selected Points Approach

Details

Type

Article

Created At

29 Dec 2024