Introduction to the expansion of the Fréchet distribution in neutrosophic logic: Properties, estimation and performance evaluation

This study introduces a novel four-parameter statistical distribution, termed the Neutrosophic Gompertz-Fréchet (NGF) distribution, which integrates neutrosophic logic with the Gompertz family and is derived from the Fréchet distribution. The direct approach is employed to construct the neutrosophic family alongside the T-X method, subsequently combining the resulting probability mass function with the fundamental Fréchet distribution to formulate the proposed model. The study examines several core statistical and mathematical properties of the NGF distribution. Parameter estimation is carried out using three techniques: the maximum likelihood method, the least squares method, and the weighted least squares method. To assess the estimation accuracy of the NGF distribution, Monte Carlo simulations are performed to compute the bias, squared errors, and root mean square errors. Lastly, a practical evaluation is conducted using two sets of real neutrosophic data to determine the efficacy of the proposed distribution. A comparative analysis is carried out between the NGF distribution and six alternative distributions using six statistical criteria, with the findings underscoring the flexibility and efficiency of the NGF distribution.