Neutrosophic Wald Distribution with Applications to Reliability Analysis
In this article, we develop neutrosophic extension of the Wald (Inverse Gaussian) distribution to present more realistic modelling for real data by introducing uncertainty in its parameters. We derive fundamental statistical properties such as the probability density function (PDF), cumulative distr...
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| Format: | Article |
| Language: | English |
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University of New Mexico
2025-05-01
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| Series: | Neutrosophic Sets and Systems |
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| Online Access: | https://fs.unm.edu/NSS/17WaldDistribution.pdf |
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| author | Afrah Al Bossly Adnan Amin |
| author_facet | Afrah Al Bossly Adnan Amin |
| author_sort | Afrah Al Bossly |
| collection | DOAJ |
| description | In this article, we develop neutrosophic extension of the Wald (Inverse Gaussian) distribution to present more realistic modelling for real data by introducing uncertainty in its parameters. We derive fundamental statistical properties such as the probability density function (PDF), cumulative distribution function (CDF) and quantile function, and compare it with the classical model. This comparison shows the versatility and great robustness of the neutrosophic model against the imprecise data. Considering that the Wald distribution plays a significant role in the theory of reliability, we extend some key reliability functions into a neutrosophic framework. Under neutrosophic uncertainty, we derive and study the survival function, the reliability function and the hazard function which results in a more generalized and pragmatic approach for modeling reliability. These functions provide an improved decision-making process for situations in which classical models are unable to capture the inbuilt uncertainties of systems. To make it even more applicable, we propose an approach to generate random samples from neutrosophic Wald distribution using quantile function so that neutrosophic Wald distribution can be simulated and empirically validated. In addition, we also develop an estimation procedure through the method of moments (mom), which shows a simple way of estimating the parameters. |
| format | Article |
| id | doaj-art-e7730efc4739448abdd8ae28fb477276 |
| institution | Kabale University |
| issn | 2331-6055 2331-608X |
| language | English |
| publishDate | 2025-05-01 |
| publisher | University of New Mexico |
| record_format | Article |
| series | Neutrosophic Sets and Systems |
| spelling | doaj-art-e7730efc4739448abdd8ae28fb4772762025-08-25T08:31:21ZengUniversity of New MexicoNeutrosophic Sets and Systems2331-60552331-608X2025-05-018227628810.5281/zenodo.14969548Neutrosophic Wald Distribution with Applications to Reliability AnalysisAfrah Al Bossly Adnan AminIn this article, we develop neutrosophic extension of the Wald (Inverse Gaussian) distribution to present more realistic modelling for real data by introducing uncertainty in its parameters. We derive fundamental statistical properties such as the probability density function (PDF), cumulative distribution function (CDF) and quantile function, and compare it with the classical model. This comparison shows the versatility and great robustness of the neutrosophic model against the imprecise data. Considering that the Wald distribution plays a significant role in the theory of reliability, we extend some key reliability functions into a neutrosophic framework. Under neutrosophic uncertainty, we derive and study the survival function, the reliability function and the hazard function which results in a more generalized and pragmatic approach for modeling reliability. These functions provide an improved decision-making process for situations in which classical models are unable to capture the inbuilt uncertainties of systems. To make it even more applicable, we propose an approach to generate random samples from neutrosophic Wald distribution using quantile function so that neutrosophic Wald distribution can be simulated and empirically validated. In addition, we also develop an estimation procedure through the method of moments (mom), which shows a simple way of estimating the parameters. https://fs.unm.edu/NSS/17WaldDistribution.pdfneutrosophic distributionneutrosophic probabilityestimationsimulation |
| spellingShingle | Afrah Al Bossly Adnan Amin Neutrosophic Wald Distribution with Applications to Reliability Analysis Neutrosophic Sets and Systems neutrosophic distribution neutrosophic probability estimation simulation |
| title | Neutrosophic Wald Distribution with Applications to Reliability Analysis |
| title_full | Neutrosophic Wald Distribution with Applications to Reliability Analysis |
| title_fullStr | Neutrosophic Wald Distribution with Applications to Reliability Analysis |
| title_full_unstemmed | Neutrosophic Wald Distribution with Applications to Reliability Analysis |
| title_short | Neutrosophic Wald Distribution with Applications to Reliability Analysis |
| title_sort | neutrosophic wald distribution with applications to reliability analysis |
| topic | neutrosophic distribution neutrosophic probability estimation simulation |
| url | https://fs.unm.edu/NSS/17WaldDistribution.pdf |
| work_keys_str_mv | AT afrahalbossly neutrosophicwalddistributionwithapplicationstoreliabilityanalysis AT adnanamin neutrosophicwalddistributionwithapplicationstoreliabilityanalysis |