Semi-minimax estimations on the exponential distribution under symmetric and asymmetric loss functions

Abstract EN

In this paper the semi-minimax estimators of the scale parameter of the exponential distribution are presented by applying the theorem of Lehmann under symmetric (quadratic) loss function and asymmetric (entropy, mlinex , precautionary) loss functions .The results of comparison between these estimators are compared empirically using Monte-Carlo simulation study with respect to the mean square error(MSE) and the mean percentage error(MPE).

In general, the results showed that the semi-minimax estimator under quadratic loss function is the best estimator by MSE and MPE for all sample sizes.

We can notice that, when the values of the parameters β ,θ increasing the semi-minimax estimator under quadratic loss function is the best estimator by MSE while comparison by MPE showed that the semi-minimax estimator under mlinex loss function when the value of c positive is the best, but they both get worse as α ,θ increases.

Also the results showed that when α, β together increase the semi-minimax