  In this paper, we introduce a new three-parameter distribution based on the
combination of re-parametrization of the so-called EGNB2 and transmuted
exponential distributions. This combination aims to modify the transmuted
exponential distribution via the incorporation of an additional parameter,
mainly adding a high degree of flexibility on the mode and impacting the
skewness and kurtosis of the tail. We explore some mathematical properties of
this distribution including the hazard rate function, moments, the moment
generating function, the quantile function, various entropy measures and
(reversed) residual life functions. A statistical study investigates estimation
of the parameters using the method of maximum likelihood. The distribution
along with other existing distributions are fitted to two environmental data
sets and its superior performance is assessed by using some goodness-of-fit
tests. As a result, some environmental measures associated with these data are
obtained such as the return level and mean deviation about this level.
