Neutrosophic Lognormal Distribution with Applications in Complex Data Modeling

This study develops a new version of the lognormal distribution, the neutrosophic lognormal distribution (NLND), to address uncertainties commonly exist in reliability studies within the engineering field. The NLND is suitable for analyzing complex data with symmetrical or right-skewed patterns. The paper discusses the mathematical characteristics of the NLND, including concepts of reliability like mean time failure, hazard rate, cumulative failure rate, and reliability function. The model is based on real-life examples from life-test data and uses the maximum likelihood method to determine two key parameters. A simulation experiment was conducted to evaluate the accuracy of the estimated parameters, showing that maximum likelihood estimators can effectively estimate unknown parameters, especially with a large sample size. Finally, a real-world data is used to demonstrate the adequacy of the proposed model in a practical scenario.