COMPARISON OF TWO METHODS FOR ESTIMATING TWO-PARAMETER EXPONENTIAL DISTRIBUTION

There have been ongoing search to find efficient, unbiased and minimal variance estimators. This paper is on the comparison of the regular Maximum Likelihood Estimator (MLE) and Penalized Maximum Likelihood Estimator (PMLE) of two-parameter Exponential distribution; the location (ϒ) and scale (λ) parameter. PMLE is obtained by adding the penalty to the regular MLE. Both bias and mean squared error of the estimators are calculated for small, medium and large samples using simulated data sets. It was observed that the penalized estimators are superior to regular MLEs as sample size (n) becomes large in terms of bias; whereas for MSE, is better than regular MLE for estimation of the location parameter. The PMLE is however not much better for the scale parameter. Based on this, the use of PMLE is recommended.