Neutrosophic Lindley Distribution: Simulation, Application, and Comparative Study

Classical statistical methods are commonly applied in distribution theory across various disciplines; however, they often fall short in addressing uncertainty, imprecision, and indeterminacy. In situations when classical distributions fail, such as when there is uncertainty, ambiguity, or missing information, the neutrosophic lindley distribution (NLiD) is important because it models indeterminate data. The classical Lindley distribution is extended by incorporating neutrosophic notions, providing flexibility for methods of ambiguous inference. Applications involving reliability analysis, risk management, and other domains with internal data uncertainties are especially well-suited for NLiD. This paper introduces the neutrosophic Lindley distribution (NLiD) to incorporate imprecision into the statistical framework. We derive key properties of the NLiD, including survival, hazard, and reverse hazard functions, as well as the odds ratio, Mills ratio, mean, and variance. Additionally, we explore entropy measures such as Neutrosophic Renyi, Neutrosophic Tsallis, and Neutrosophic Arimoto entropies, complemented by a simulation study and graphical analysis. Maximum likelihood estimation is employed to estimate the distribution parameters, with simulation validating the accuracy of these estimates. Our findings reveal that the proposed distribution can exhibit symmetric, left-skewed, and right-skewed characteristics. An empirical evaluation using a on dioxin consumption in food demonstrates that the proposed model is effective and practical for real-world application.