A New Generalization of the Inverted Gompertz Distribution with Different Methods of Estimation and Applications

Designing appropriate models for analyzing data in various fields is essential as it helps professionals comprehend complex data patterns and their characteristics, leading to informed decision-making. Despite the diversity of probability distribution, the data may not conform to classical distributions in many instances. Consequently, there arises a need for a new distribution that can accommodate the intricacies of diverse data forms and enhance the goodness of fit. This article introduces a novel extended lifetime model called the new exponential exponentiated generalized inverted Gompertz based on the new exponential-X family of distributions. The article discusses some statistical properties associated with the proposed distribution. The parameters of the new distribution are estimated using multiple estimation techniques, and their performance is compared through Monte Carlo simulations. The demonstrated potential and effectiveness of the proposed distribution are exemplified by its application to three datasets within various fields.