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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Main Authors: Afrah Al Bossly, Adnan Amin
Format: Article
Language:English
Published: University of New Mexico 2025-05-01
Series:Neutrosophic Sets and Systems
Subjects:
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.
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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