Extension of the heavy-tailed distribution with applications in medical sciences

Heavy-tailed-Type II Exponentiated Half Logistic-Gompertz-G (HT-TIIExHL-G-G) class of distributions is proposed in this article. The structural properties of the distribution are thoroughly explored, and specific cases within this family are presented. We carried out simulation study to explore the estimation of the model parameters through several established techniques. The analysis showcased their numerical efficiency and performance. Furthermore, through the utilization of maximum likelihood technique, we use a specific instance from the HT-TIIExHL-G-G family of distributions (FD) to show its practical application. This is achieved by fitting it to three real-world data examples from health care and engineering disciplines.