The discussion revolves around the broader concept of exponential family distributions, exploring their applications in survival analysis and reliability engineering. Various distributions within this family, such as the Weibull, Rayleigh, and Gompertz distributions, are examined in terms of their suitability for modelling different phenomena, including instantaneous failure events, independent sums of events, and decreasing processes over time. Additionally, a newly derived distribution, termed the Meenakshi’s-Gompertz distribution, is introduced, with its parameters interchangeably representing scale and shape properties.
Meenakshi et al. (Thu,) studied this question.