Analyzing Chemical Decay in Environmental Nanomaterials Using Gamma Distribution with Hybrid Censoring Scheme
This study addresses the challenges of estimating decay times for chemical components, focusing on hydroxylated fullerene <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>C</mi>&...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2024-11-01
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| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/12/23/3737 |
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| Summary: | This study addresses the challenges of estimating decay times for chemical components, focusing on hydroxylated fullerene <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>C</mi><mn>60</mn></msub><msub><mrow><mo>(</mo><mi>O</mi><mi>H</mi><mo>)</mo></mrow><mn>29</mn></msub></mrow></semantics></math></inline-formula>, 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. |
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| ISSN: | 2227-7390 |