In practice there does exist some data sets with extreme values like in environmental sciences, and engineering etc. If we deal with such type of datasets with the classical methods, then the results may not be more efficient as compared to the specialized methods. This paper concentrated on the analysis of the real data sets with extreme and without extreme values by using probability distributions. It has been determined that the Flexible Exponential Type Exponential (FETE) distribution performs well as compared to others in both cases. Various statistical properties (r^th moments, survival function, hazard function, etc) and a simulation study is conducted on the efficient model. Furthermore, the proposed model is proficient to display the non-monotonic hazard rate with the lifetime data. The parameters are estimated using maximum likelihood method.

Index Terms- Exponential distribution, FE, Modelling, Statistical Properties.