The Neutrosophic Gompertz-G Family: Analytical Properties, Simulation Studies, and Applications to Real Data

Abstract

This research deals with finding a family of continuous distributions according to neutrosophic logic called neutrosophic Gompertz-G (NGo-G), where the Gompertz family is obtained according to the T-X method and then merging the family using the direct method of neutrosophic logic to obtain it. The study also provides a detailed analysis of the statistical characteristics of the family of distributions, then using the exponential distribution according to this family to obtain a new distribution consisting of three neutrosophic parameters and neutrosophic variable called a neutrosophic Gompertz exponential (NGoE), in addition to reviewing the basic characteristics of NGoE, and providing a comprehensive analysis of the characteristics of the new distribution and estimate its parameters. In addition, a Monte Carlo simulation of the new distribution is carried out in order to validate its characteristics and guarantee that it is accurate prior to the implementation of our suggested model estimator. In addition, the distribution is applied to two different kinds of real data, and then the results of the new distribution are compared with the results of other distributions using two different informatics standards. This is done in order to determine the effectiveness of the distribution in modeling, as well as to demonstrate that it is superior to well-known models from the literature when it comes to fitting these real data sets.