Conclusion
This paper can be considered as a starting point for study on the new threeparameter
lifetime distribution, the CR- distribution, which relates to three known twoparameter
distributions. We provided the closed forms of the characteristic function,
moment generating function (including their existing conditions), and the cumulative
distribution function of CR- distribution based on the new parametrization. The existing
condition of the moment generating function depends on parameter only.
There are still many topics on CR- distribution to investigate, such as statistical
inference and the survival analysis. It will give us more results if we can join the statistical
knowledge and the engineering knowledge on this subject