A new flexible odd type-G family of distributions with properties and applications in the biomedical sector.

In this paper, we propose a new family of probability distributions called the new flexible odd type-G family of distributions. We have used the Weibull distribution as the base reference to introduce a new heavy-tailed distribution, which we have fittingly named the new flexible odd-type Weibull distribution. The hazard function of the newly proposed distribution exhibits various shapes, such as increasing, decreasing, unimodal, S-shaped, J-shaped, reverse J-shaped, and bathtub shapes. For the proposed distribution, we have derived various distributional properties, including moments, moment generating function, characteristic function, mean deviation from median, and order statistics. Furthermore, actuarial measures, such as Value at Risk and Tail Value at Risk, are calculated, and it is empirically demonstrated that the proposed distribution exhibits heavy-tailed behavior. To estimate the model parameter, we applied the maximum likelihood estimation method and conducted a simulation study to assess its performance for the proposed distribution. From the simulation results, it is confirmed that as the sample size increases, the mean square error and biases decrease and approach zero. Finally, we evaluated three real data sets from the biomedical field to demonstrate the flexibility and superiority of the proposed distribution in comparison to the other nine probability distributions. The analyzed results (numerically as well as graphically) show that the newly proposed model provides a superior fit compared to the competing distributions.