Neutrosophic Gompertz Distribution: Applications in Analyzing Complex Environmental Datasets

Many real-world problems are characterized by uncertainty, indeterminacy, vagueness, and ambiguity. In situations where the random variable has ambiguous values, classical probability distributions may not be effective. Instead, neutrosophic probability distributions often yield better results. The Gompertz distribution, widely applied across various fields, is extended in this research to introduce the neutrosophic Gompertz distribution (NGoD) for modeling ambiguous data. Key neutrosophic properties such as moments, Shannon entropy, and reliability measures of NGoD are derived. Neutrosophic parameters are estimated using maximum likelihood estimation, and a simulation study is conducted to examine parameter behavior and compare the indeterminacy between parameters. Finally, the NGoD is applied to two real-world ambiguous data sets, demonstrating the effectiveness and suitability of the neutrosophic Gompertz distribution in uncertain contexts. The analysis shows that the neutrosophic Gompertz model is appropriate, reasonable, and useful for such applications.