A Novel Distribution in the Family of Lifetime Distributions for Enhancing Predictive Modeling for Medical and Engineering Data

Abstract

In nearly all scientific disciplines, the statistical inference about the population rely on handling the sampled data. In the time to event analysis, there are many lifetime distributions to model variation of the lifetime observations based on the shape of hazard rate of the data. In the literature, it has been observed that for non-monotonic hazard the existing distributions do not provide good fits. Practically it is not possible for a distribution to fit any kind of data. Therefore, in this study, a new lifetime distribution is suggested called Flexible Exponentiated Weibull distribution (FEW) to model monotonic and non-monotonic hazard rate data. Maximum likelihood estimation approach is used to estimate the model parameters. In addition to these some prominent statistical properties like, reliability function, moments, hazard function, order statistics, quantile function and entropy measure are obtained. Two real data sets were taken to compare the proposed distribution with existing distributions, and the results showed that the proposed distribution is more flexible than other existing lifetime distributions. Furthermore, simulation study is carried out to check the consistency of model parameters that showed that the parameters are consistent when the sample size increases. These results establish a foundational rationale for selecting the suggested distribution as a model for such a data type. It shows that this distribution is more flexible and suitable for the data studied, making a strong case for choosing it over other options. These findings not only boost trust in the chosen model but also help in deciding how to model similar data in the future.