The New Extended-X Exponentiated Inverted Weibull Distribution: Statistical Inference and Application to Carbon Data

Developing novel probability distributions holds significant importance in contemporary society across various domains. In this study, we introduce a distinctive continuous lifespan model characterized by three parameters, achieved through integrating the Extended-X Exponentiated (NEX) family core with the foundational Exponentiated Inverted Weibull (EIW) distribution. This amalgamation yields a novel distribution, termed the New Extended-X Exponentiated InvertedWeibull (NEEIW) distribution. Notably, the NEEIW distribution exhibits favorable attributes facilitated by its straightforward linear representation of hazard rate function, moments, and moment-generating function, alongside the provision of stress-strength reliability in concise closed forms. Parameter estimation for the NEEIW model is conducted via conventional methodologies such as maximum likelihood estimation (MLE) and maximum product of spacing (MPS), supplemented by exploring non-classical Bayesian analytical approaches. The empirical validation of the proposed distribution is conducted using two distinct carbon datasets, substantiating its superiority and applicability in modeling real-world data.