The quality of the procedures used in a statistical analysis depends heavily on the assumed probability model or distribution. Because of it, considerable effort has been expended in the development of large classes of standard probability distributions along with relevant statistical methodologies. However, there still remain many important problems where the real data does not follow any of the classical or standard probability models.
Because of having only one parameter, the Lindley distribution does not provide enough flexibility for analyzing different types of lifetime data. To increase the flexibility for modelling purposes it will be useful to consider further alternatives of this distribution.
This has motivated the researcher to consider two new distributions. One of them is based on a certain mixtures of the gamma distributions, while the other model is stemming from the Lindley distribution as the underlying distribution. Moreover, the two new models can accommodate both decreasing and increasing failure rates as its antecessors, as well as unimodal and bathtub shaped failure rates.