Fitting various medical and engineering applications using the new lifetime distribution with a mathematical framework

Sustainability considerations play a crucial role in informing the modeling and fitting of medical and engineering data, ensuring the development of robust and environmentally conscious solutions. This paper delves into the investigation of a novel continuous distribution, aiming to provide a thorough understanding of its various fundamental mathematical and statistical properties. The analysis encompasses an exploration of survival functions, hazard rate functions, quantile, skewness, kurtosis, moments, mean time to failure, mean time to repair, insurance pricing principles, availability, and mean residual (past) lifetime functions. The proposed model demonstrates versatility in modeling both asymmetric and symmetric data across various kurtosis shapes. It can effectively handle outlier observations and accommodate different shapes of failure rates, including unimodal, bathtub, increasing, or decreasing patterns. This makes the proposed model suitable for modeling data in diverse fields. The maximum likelihood approach is employed to estimate model parameters using complete and upper recorded values. A simulation study is conducted to evaluate the performance of the estimators under different sample sizes for both complete and upper recorded values. To further demonstrate the flexibility and effectiveness of the new model, two datasets from medical and engineering domains are utilized for validation and testing purposes.