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Analyzing Chemical Decay in Environmental Nanomaterials Using Gamma Distribution with Hybrid Censoring Scheme

Author

Listed:
  • Hanan Haj Ahmad

    (Department of Basic Science, The General Administration of Preparatory Year, King Faisal University, Hofuf 31982, Saudi Arabia
    Department of Mathematics and Statistics, College of Science, King Faisal University, Al-Ahsa 31982, Saudi Arabia)

  • Dina A. Ramadan

    (Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 33516, Egypt)

  • Mohamed Aboshady

    (Department of Basic Science, Faculty of Engineering, The British University in Egypt, El Sherook City 11837, Cairo, Egypt)

Abstract

This study addresses the challenges of estimating decay times for chemical components, focusing on hydroxylated fullerene C 60 ( O H ) 29 , which poses potential environmental risks due to its persistence and transformation in soil. Given the complexities of real-world experiments such as limited sample availability, time constraints, and the need for efficient resource use, a framework using the Gamma distribution based on hybrid Type-II censoring schemes was developed to model the decay time. The Gamma distribution’s flexibility and mathematical properties make it well-suited for reliability and decay analysis, capturing variable hazard rates and accommodating different censoring structures. We employ maximum likelihood estimation (MLE) and Bayesian methods to estimate the model’s parameters, consequently estimating the reliability and hazard functions. The large sample theory for MLE is used to approximate variances for constructing asymptotic confidence intervals. Additionally, we utilize the Markov chain Monte Carlo technique within the Bayesian framework to ensure robust parameter estimation. Through simulation studies and statistical tests—such as Chi-Square, Kolmogorov–Smirnov, and others—we assess the Gamma distribution’s fit and compare its performance with other distributions, validating the proposed model’s effectiveness.

Suggested Citation

  • Hanan Haj Ahmad & Dina A. Ramadan & Mohamed Aboshady, 2024. "Analyzing Chemical Decay in Environmental Nanomaterials Using Gamma Distribution with Hybrid Censoring Scheme," Mathematics, MDPI, vol. 12(23), pages 1-17, November.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:23:p:3737-:d:1531213
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    References listed on IDEAS

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    1. Maha A. Aldahlan & Rana A. Bakoban & Leena S. Alzahrani, 2022. "On Estimating the Parameters of the Beta Inverted Exponential Distribution under Type-II Censored Samples," Mathematics, MDPI, vol. 10(3), pages 1-37, February.
    2. Nanami Taketomi & Kazuki Yamamoto & Christophe Chesneau & Takeshi Emura, 2022. "Parametric Distributions for Survival and Reliability Analyses, a Review and Historical Sketch," Mathematics, MDPI, vol. 10(20), pages 1-23, October.
    3. Leijia Ding & Wenhao Gui, 2023. "Statistical Inference of Two Gamma Distributions under the Joint Type-II Censoring Scheme," Mathematics, MDPI, vol. 11(9), pages 1-23, April.
    4. Pan, Zhengqiang & Balakrishnan, Narayanaswamy, 2011. "Reliability modeling of degradation of products with multiple performance characteristics based on gamma processes," Reliability Engineering and System Safety, Elsevier, vol. 96(8), pages 949-957.
    5. Abhimanyu Singh Yadav & Sanjay Kumar Singh & Umesh Singh, 2016. "On Hybrid Censored Inverse Lomax Distribution: Application to the Survival Data," Statistica, Department of Statistics, University of Bologna, vol. 76(2), pages 185-203.
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