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Abstract

Despite significant progress in the development of statistical distributions, there remain clear gaps in modelling complex datasets, such as those involving uncertainty or requiring flexible representations of multidimensional variables. This study introduces a new distribution the Neutrosophic Gompertz-Inverse Burr-X (NGoIB-X) distribution to address these challenges. The model is based on the Neutrosophic Gompertz family (NGo-G), which itself employs the T-X method in its formulation. Characterised by four Neutrosophic parameters and a Neutrosophic random variable, the NGoIB-X distribution offers enhanced flexibility for representing and analysing uncertain data. The theoretical properties of the NGoIB-X distribution are explored, including its Neutrosophic probability density function (NPDF), Neutrosophic cumulative distribution function (NCDF), and hazard function. Parameters estimation is conducted using three methods: maximum likelihood estimation (MLE), least squares (LS), and weighted least squares (WLS). A Monte Carlo simulation is performed to evalute the efficiency of these estimation techniques. To demonstrate practical relevance, the NGoIB-X distribution is applied to Neutrosophic data on under-five mortality rates. The proposed model achieved lowr values across model selection criteria AIC: [177.437, 177.531]; CAIC: [179.342, 179.435]; BIC: [182.470, 182.563]; HQIC: [178.887, 178.9802] compared to five alternative distributions. These results highlight the distribution's effectiveness in accurately representing complex datasets, confirming its suitability for applications in public health and applied statistics.

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