A New Insight into Reliability Data Modeling with an Exponentiated Composite Exponential-Pareto Model

Abstract

It is observed that, for some of the data in engineering and medical fields, the hazard rates increase to a high peak at the beginning and quickly decrease to a low level. In the context of survival analysis, such a hazard rate is called a upside-down bathtub hazard rate. In this paper, we investigated the properties of a model named exponentiated exponential-Pareto distribution. The model was recently proposed and applied to insurance data. We demonstrated that the model has upside-down bathtub-shaped hazard rates with specific choices of parameters. The theoretical properties such as moments, survival functions, and hazard functions were derived. The parameter estimation procedures were also introduced. We then briefly discussed the goodness-of-fit tests of the model with the simulations. Finally, we applied the model to a specific time-to-event data set along with a comparison of the performances with previous existing models. When compared to previous proposed models, the exponentiated exponential-Pareto model demonstrated good performance when fitting to such data sets.