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Chen is suggested a two-parameter distribution. This distribution can have increasing failure rate function or a bathtub-shaped that allows it to fit real lifetime data sets. The ML (Maximum Likelihood) and Bayes estimates of the parameters of Chen’s distribution are constituted in this paper. The approximate values of Bayesian estimates are obtained by using the Tierney-Kadane approach. Two-parameter bathtub-shaped distribution's estimations are derived using Jeffrey's extension prior under General entropy, Squared and Linex loss functions. Besides, performances of ML and Bayes estimates are compared concerning MSE's (Mean Square Error) by using Monte Carlo simulation. As a result, it has been seen that approximate Bayes estimates obtained under linex loss function are better than others. Moreover, real data analysis for his distribution is presented.

Comparison of estimators under different loss functions for two-parameter bathtub - shaped lifetime distribution