Applications to medical and failure time data: Using a new extension of the extended exponential model

Abstract

This article introduces a novel extension of the extended exponential model, referred to as the Kavya-Manoharan extended exponential model. The new suggested model is very flexible model because its probability density function and hazard rate function can be right skewed, reversed J-shapes and increasing. Various statistical properties of the Kavya-Manoharan extended exponential model are calculated. Various uncertainty metrics are calculated and analyzed both theoretically and quantitatively. Furthermore, the Kavya-Manoharan extended exponential model utilizes the maximum likelihood estimation technique to determine its two parameters. A comprehensive numerical analysis is conducted to assess the effectiveness of the maximum likelihood estimation technique. The feasibility and importance of the Kavya-Manoharan extended exponential model may be demonstrated by analyzing three actual datasets about medical and failure times data. The Kavya-Manoharan extended exponential model is evaluated against many established statistical models such as; generalized Dinesh-Umesh-Sanjay-exponential, extended exponential, generalized Lindley, Kavya-Manoharan Burr X, generalized power Weibull, and the Gumbel distributions using diverse criteria. The numerical results indicated that the Kavya-Manoharan extended exponential model was more suitable for the data than the other competing models.