A New Family of Continuous Distributions with Applications

This article introduces a novel set of optimizing probability distributions known as the Survival Power-G (SP-G) family, which employs a specific approach to introduce an additional parameter with the survival function of the original distributions. The utilization of this family enhances the modelling capabilities of diverse existing continuous distributions. By applying this approach to the single-parameter exponential distribution, a new two-parameter Survival Power-Exponential (SP-E) distribution is generated. The statistical characteristics of this fresh distribution and the maximum likelihood estimator are established, and Monte Carlo simulation is utilized to explore the efficiency of the maximum likelihood estimator of the two parameters under varying sample sizes. Subsequently, the new distribution is employed in the analysis of three distinct sets of real data. Through comparison with alternative distributions on these datasets, it is demonstrated that the new distribution outperforms the other distributions.