Development of a new statistical distribution with insights into mathematical properties and applications in industrial data in KSA

Badr Aloraini; Abdulaziz S. Alghamdi; Mohammad Zaid Alaskar; Maryam Ibrahim Habadi; Badr Aloraini; Abdulaziz S. Alghamdi; Mohammad Zaid Alaskar; Maryam Ibrahim Habadi

doi:10.3934/math.2025343

AIMS Mathematics

2025, Volume 10, Issue 3: 7463-7488. doi: 10.3934/math.2025343

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Development of a new statistical distribution with insights into mathematical properties and applications in industrial data in KSA

1.
Department of Mathematics, College of Science and Humanities, Shaqra University, 11961 Shaqra, Saudi Arabia
2.
Department of Mathematics, College of Science & Arts, King Abdulaziz University, P. O. Box 344, Rabigh 21911, Saudi Arabia
3.
Department of Accounting, College of Business Administration in Hawtat bani Tamim, Prince Sattam bin Abdulaziz University, Saudi Arabia
4.
Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia

Received: 17 December 2024 Revised: 15 March 2025 Accepted: 21 March 2025 Published: 31 March 2025
MSC : 60B12, 62G30

This study presents the development of a novel distribution through a transformation involving error functions, namely the error function inverse Weibull model, along with an overview of the fundamental characteristics of the proposed model. The hazard function of the recommended model is very flexible; it fits increasing, decreasing, and unimodal factors. For estimating the unknown parameters, we suggested two estimation methods, including the maximum likelihood estimation and Bayesian techniques. We perform a Monte Carlo simulation analysis to assess the stability of the parameter estimation procedure. The numerical results of these simulations show that the Bayesian technique under the square error loss function performs better than another method to obtain the model parameters. We thoroughly examine the significance of the proposed model and illustrate its application using three real-world data sets from the industrial sector. We compared the suitability and flexibility of the suggested distribution with several others, and the results showed that it fits the real-world data better than the competing models.
- Bayesian method,
- error function transformation,
- Hazard function,
- loss function,
- maximum likelihood estimation,
- simulation analysis
Citation: Badr Aloraini, Abdulaziz S. Alghamdi, Mohammad Zaid Alaskar, Maryam Ibrahim Habadi. Development of a new statistical distribution with insights into mathematical properties and applications in industrial data in KSA[J]. AIMS Mathematics, 2025, 10(3): 7463-7488. doi: 10.3934/math.2025343

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Abstract

This study presents the development of a novel distribution through a transformation involving error functions, namely the error function inverse Weibull model, along with an overview of the fundamental characteristics of the proposed model. The hazard function of the recommended model is very flexible; it fits increasing, decreasing, and unimodal factors. For estimating the unknown parameters, we suggested two estimation methods, including the maximum likelihood estimation and Bayesian techniques. We perform a Monte Carlo simulation analysis to assess the stability of the parameter estimation procedure. The numerical results of these simulations show that the Bayesian technique under the square error loss function performs better than another method to obtain the model parameters. We thoroughly examine the significance of the proposed model and illustrate its application using three real-world data sets from the industrial sector. We compared the suitability and flexibility of the suggested distribution with several others, and the results showed that it fits the real-world data better than the competing models.

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