  The present paper considers modified extension of the exponential
distribution with three parameters. We study the main properties of this new
distribution, with special emphasis on its median, mode and moments function
and some characteristics related to reliability studies. For Modified-
extension exponential distribution (MEXED) we have obtained the Bayes
Estimators of scale and shape parameters using Lindley's approximation
(L-approximation) under squared error loss function. But, through this
approximation technique it is not possible to compute the interval estimates of
the parameters. Therefore, we also propose Gibbs sampling method to generate
sample from the posterior distribution. On the basis of generated posterior
sample we computed the Bayes estimates of the unknown parameters and
constructed 95 % highest posterior density credible intervals. A Monte Carlo
simulation study is carried out to compare the performance of Bayes estimators
with the corresponding classical estimators in terms of their simulated risk. A
real data set has been considered for illustrative purpose of the study.
