New Modified Gompertz Probability Distribution With Flexible Hazard Functions

This paper introduces a new probability model called the modified Gompertz distribution from the base Gompertz distribution by combining its hazard function with first and second degree polynomial (linear and quadratic) functions. The new probability model is found to have more flexible hazard shapes with strictly increasing, strictly decreasing, and bumping behaviors. Properties of the new probability model are derived and discussed. Simulation studies and data fitting are conducted. The modified Gompertz distribution is found to fit better to four datasets as compared to the base Gompertz distribution and also six other models which are Topp-Leone Gompertz, Generalized Gompertz, Exponentiated Gompertz Exponential, Power Gompertz, Gompertz Ampadu Lomax, and Exponential Generalized Extended Gompertz probability distributions. The modified Gompertz distribution is a contribution to the field of statistical theory, having very interesting shapes of hazard function can have applications to survival, waiting time, and reliability data analyses. Any statistical inference from simulation study and data fitting to real-world data can possibly lead to new knowledge in applied probability, statistics, and application field such as life science, health, and engineering. Generalization to higher order polynomial functions is recommended for future research. Applications of the models to data from various fields can be studied.