Development of the gompertz-neutrosophic lomax distribution: A four-parameter expansion for modeling uncertainty

This work presents new continuous distribution derivative from the classical Lomax distribution by two parameters, which is extended to four-parameter model by mixing the Gompertz-Neutrosophic (NGo) family. The new proposed model, named Gompertz-Neutrosophic Lomax Distribution (NGoLoD), by mixing elements from neutrosophic logic of NGo family into the extended Neutrosophic Lomax model. This development is a part of an work effort to improve the flexibility for Lomax distributions for treating problems of complex real data that exhibit volatility, and uncertainty. The NGoLoD is defined through finding its Neutrosophic CDF and Neutrosophic pdf, these functions reflect the dual nature of the model's parameters for Troth, falsity, and uncertainty components giving the flexible distribution that can adapt to varying degrees of uncertainty. Several mathematical properties of NGoLoD are explored, including the survival function, hazard function, moments, and some other properties. The neutrosophic parameters significantly expansions the flexibility of the model, allowing it to accommodate a wide a range of data behaviors. To show activity of the NGoLoD to estimation introduced three estimation techniques: Maximum Likelihood Estimation (MLE), Least Squares Estimation (LSE), and Weighted Least Squares Estimation (WLSE), also it was used these techniques to work simulation for different size of samples to show which technique is better and known NGoLoD ability for estimation. To demonstrate ability of NGoLoD, the model is applied to neutrosophic real-world data, and performance of NGoLoD distribution is compared against five other distributions, using some criteria Verification.