Delta Power Transformation: A New Family of Probability Distributions

This research article presents a novel approach called the delta-power transformation, which introduces a new class of lifetime distributions. The article discusses the key features of one member from this family, which exhibits a hazard function with a distinctive shape resembling a J, reverse-J, constant, or monotonically increasing. The researchers delve into the statistical characteristics of this distribution and utilize the maximum likelihood estimation (MLE) approach to gauge its parameters. They conduct a simulation experiment to evaluate the precision of the estimation process, finding that biases and mean square errors diminish with larger sample sizes, even in cases involving small samples. Moreover, the study show-cases the practical utility of the suggested distribution through an examination of two real-world datasets. Evaluation criteria for model selection and goodness-of-fit test statistics indicate that the proposed model surpasses certain existing models in performance.