The Gompertz distribution is widely used in medical and reliability studies, particularly for modeling mortality rates and failure data. However, it has limitations in capturing complex data behaviors, such as heavy tails and varying hazard rate shapes. This paper introduces the Odd Beta Prime-Gompertz (OBP-Gompertz) distribution, a four-parameter extension of the traditional Gompertz model. The OBP-Gompertz distribution offers flexibility in modeling various shapes of probability density functions, including right-skewed, left-skewed, heavy-tailed, light-tailed, and unimodal distributions. Its hazard function can accommodate multiple forms, such as increasing, decreasing, bathtub-shaped, and inverted bathtub-shaped curves, making it well-suited for mortality rate data. The paper investigates key statistical properties, including moments, moment generating function, quantile function, Rényi and Tsallis entropy measures. Parameters are estimated using maximum likelihood estimation, and the model's robustness is assessed through Monte Carlo simulations. The OBP-Gompertz model is applied to three real-world COVID-19 mortality datasets from China, the Netherlands, and Nepal. The results demonstrate that the OBP-Gompertz model provides superior fits compared to the traditional Gompertz and other models. This work highlights the OBP-Gompertz distribution as a valuable tool for survival analysis, reliability studies, and epidemiological research.
Suleiman et al. (Mon,) studied this question.